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          JULIAN MARQUEZ v. COMMISSIONER
                  OF CORRECTION
                     (SC 19889)
           Palmer, McDonald, Robinson, D’Auria and Kahn, Js.*

                                   Syllabus

The petitioner sought a writ of habeas corpus, claiming that the state had
    violated his due process rights by not disclosing an alleged leniency
    agreement between the state and S, an accomplice who testified against
    the petitioner at his criminal trial, in violation of Brady v. Maryland
    (373 U.S. 83) and its progeny, and by failing to correct S’s allegedly false
    testimony that no such agreement existed. At the petitioner’s criminal
    trial, S testified that it was the petitioner who fatally shot the victim
    during an armed robbery and that he did not know if he would receive
    any kind of consideration from the state as a result of testifying. In
    addition, the prosecutor denied that the state had entered into any formal
    agreement with S in exchange for his testimony. After the petitioner
    was convicted of felony murder, the state declined to prosecute S for
    felony murder. The habeas court denied the petitioner’s habeas petition,
    concluding, inter alia, that no arrangement existed between the state
    and S that had to be disclosed under Brady. The habeas court denied
    the petition for certification to appeal, and the petitioner appealed to the
    Appellate Court, which dismissed the petitioner’s appeal. The Appellate
    Court concluded that the habeas court did not abuse its discretion in
    denying the petition for certification to appeal, and the petitioner
    appealed to this court, claiming that, contrary to the determination of
    the habeas court and the Appellate Court, the state had an agreement
    with S that it had not disclosed to the petitioner in violation of Brady.
    The respondent, the Commissioner of Correction, countered that,
    although plea discussions between the state and S occurred, there was
    no Brady violation because no agreement was ultimately formalized,
    and, in any event, S’s testimony was immaterial. Held:
1. This court declined to address the issue of whether the habeas court had
    abused its discretion in denying certification to appeal, there having
    been an alternative basis on which to uphold the habeas court’s decision;
    the petitioner could not have obtained the relief he requested in his
    habeas petition even if he were to prevail on the issue addressed by
    the habeas court of whether there had been a leniency agreement
    between the state and S.
2. This court concluded that, even if the state improperly had failed to
    disclose the alleged leniency agreement it had reached with S, there
    was no reasonable likelihood that full disclosure of that agreement or
    the prosecutor’s failure to correct S’s allegedly false testimony concern-
    ing such an agreement would have affected the judgment of the jury,
    and, accordingly, there was no due process violation because the lack
    of any disclosure was immaterial under Brady: the state’s case against
    the petitioner was overwhelming, as the petitioner admitted in a state-
    ment to the police that he had been present at the murder scene and had
    held the gun that had been used in the shooting, multiple eyewitnesses
    identified the petitioner as the shooter, the petitioner had confessed to
    a fellow inmate that he had shot the victim, and the state presented
    consciousness of guilt evidence by entering into evidence a letter written
    by the petitioner; moreover, S’s testimony corroborated other evidence
    introduced at trial, rendering much of S’s testimony duplicative, and S
    was thoroughly impeached on cross-examination.
3. This court declined the petitioner’s request to invoke its supervisory
    authority over the administration of justice and to adopt a rule requiring
    that the state disclose any representations by a state’s attorney, made to
    a cooperating witness or his attorney, concerning the potential ultimate
    disposition of the witness’ pending criminal case before the witness tes-
    tifies.
                      (One justice concurring separately)
       Argued March 26, 2018—officially released January 15, 2019
                     Procedural History

  Amended petition for a writ of habeas corpus,
brought to the Superior Court in the judicial district
of Tolland and tried to the court, Fuger, J.; judgment
denying the petition; thereafter, the court denied the
petition for certification to appeal, and the petitioner
appealed to the Appellate Court, DiPentima, C. J., and
Mullins and Foti, Js., which dismissed the appeal, and
the petitioner, on the granting of certification, appealed
to this court. Affirmed.
  James E. Mortimer, assigned counsel, for the appel-
lant (petitioner).
  Sarah Hanna, assistant state’s attorney, with whom,
on the brief, were Gail P. Hardy, state’s attorney, and
Angela Macchiarulo, senior assistant state’s attorney,
for the appellee (respondent).
                         Opinion

   D’AURIA, J. In this certified appeal, we are asked to
consider whether the state violated the due process
rights of the petitioner, Julian Marquez, by not disclos-
ing an alleged agreement between the state and Edwin
Soler, a testifying accomplice in the petitioner’s under-
lying criminal case, and by failing to correct Soler’s
allegedly false testimony that no such agreement
existed. The state charged the petitioner and Soler with
felony murder and robbery related charges following
the murder of Miguel Delgado, Jr., during the course of
a robbery at Delgado’s apartment. After Soler provided
testimony implicating the petitioner as the person who
murdered Delgado, and after the petitioner was con-
victed of felony murder, the state declined to prosecute
the felony murder charge against Soler. Although the
prosecutor denied during the petitioner’s criminal trial
that the state had entered into any formal arrangement
with Soler in exchange for his testimony, he acknowl-
edged that he had presented to Soler’s attorney poten-
tial ‘‘hypothetical’’ outcomes that could come about if
Soler were to testify truthfully against the petitioner.
   On appeal to this court, the petitioner asks us to
conclude, contrary to the determination of the habeas
court and the Appellate Court; Marquez v. Commis-
sioner of Correction, 170 Conn. App. 231, 240, 154 A.3d
73 (2017); that the state had an agreement with Soler
that it had not disclosed to the petitioner in violation
of Brady v. Maryland, 373 U.S. 83, 87, 83 S. Ct. 1194,
10 L. Ed. 2d 215 (1963); see also Giglio v. United States,
405 U.S. 150, 153, 92 S. Ct. 763, 31 L. Ed. 2d 104 (1972);
Napue v. Illinois, 360 U.S. 264, 269, 79 S. Ct. 1173, 3 L.
Ed. 2d 1217 (1959); and in contravention of the four-
teenth amendment to the federal constitution. U.S.
Const., amend. XIV, § 1. The petitioner also asks us to
conclude that the nondisclosure of this agreement was
‘‘material,’’ warranting the relief he sought from the
habeas court.
  We do not consider whether the state had an undis-
closed deal with Soler because, even if we assume that
such an agreement was struck, we are nonetheless per-
suaded that there is no reasonable likelihood that dis-
closure of the agreement would have affected the
judgment of the jury. Consequently, we conclude that
there was no due process violation because the lack of
any disclosure was immaterial under Brady v. Mary-
land, supra, 373 U.S. 87, and, therefore, we affirm the
judgment of the Appellate Court on that alternative
basis.
                            I
                            A
  At the petitioner’s criminal trial, the state presented
evidence to establish the following facts, as recounted
State v. Marquez, 291 Conn. 122, 967 A.2d 56, cert.
denied, 558 U.S. 895, 130 S. Ct. 237, 175 L. Ed. 2d 163
(2009). In 2003, two friends, Mark Clement and Christo-
pher Valle, were visiting Delgado, a mutual friend, at
Delgado’s apartment in Hartford, where the robbery
and murder took place. Id., 126. Others joined them to
socialize at the apartment, as was the regular practice
on the weekends at this location. Id.
   The front door of the apartment opened to the living
room, and the apartment had a small game room and
a kitchen connected to the living room. Id., 126–27.
On the evening of the murder, the living room was
illuminated only indirectly by light emanating from the
kitchen and the game room. Id., 127. There was a couch
on the back wall of the living room that faced the front
door. Id. The front door opened into a lighted common
hallway. Id., 126.
   Several people visited the apartment intermittently
throughout the night, while Delgado, Clement and Valle
primarily remained in the game room playing games
and drinking alcoholic beverages. Id., 127. At around
midnight, Valle was preparing to leave the apartment
when he exited the game room to say goodbye to Del-
gado, who was standing just inside the front door
attempting to get rid of two men who stood in the
hallway. Id. As Valle approached the front door, he saw
someone with a gun in the hallway and described him
as a Hispanic male in his early twenties, wearing braids
and black clothing. Id. The gunman then pointed a hand-
gun directly at Valle and entered the apartment, along
with another man. Id.
   Valle, Delgado, Clement, and one other man present
in the apartment were ordered to sit down on the couch.
Id. After the men were gathered on the couch in the
living room, the two intruders were only a few feet
away for a period of several minutes. Id. Both Valle and
Clement had multiple opportunities to see the intruders’
faces. Id., 127–28. Valle saw the gunman’s face in the
brightly lit hallway prior to his entrance into the apart-
ment and, when Valle was seated in the living room,
saw the gunman’s face illuminated by light from the
kitchen. Id., 128. Clement first saw the gunman’s face
when the gunman entered the apartment and briefly
walked into the lighted game room, and, again, when
they were all in the living room that was illuminated
by the kitchen light. Id.
   The intruders ordered the men to surrender their
valuables, which they did. Id. The intruders were dissat-
isfied with Delgado’s offer of a small amount of mari-
juana, believing Delgado had money and drugs
elsewhere in the apartment. Id. When the intruders
sought access to the bedroom of the apartment, which
was attached to the kitchen, Delgado suddenly rushed
the gunman and grabbed him, causing a struggle to
ensue between Delgado and the gunman. Id., 127–28.
Three shots rang out, and Clement and Valle fled to the
game room as Delgado fell to the floor. Id., 128. When it
was apparent that the intruders had fled, Valle emerged
from the game room to discover Delgado lying in a pool
of blood and called the police. Id. When the police
arrived, both Valle and Clement stated that they would
be able to identify the gunman. Id., 128–29.
  Four days later, while making his regular visit to his
parole officer, Valle observed the petitioner at the parole
office, and immediately recognized him as the gunman.
Id., 129. He reported this to office personnel, who con-
veyed the information to the detective who was leading
the investigation into the incident. Id. On the basis of this
information, the detective presented Valle with a photo-
graphic array consisting of eight photographs fitting the
description Valle provided, including one photograph of
the petitioner. Id. Valle immediately selected the photo-
graph of the petitioner. Id., 130.
   Several days later, the detective contacted Clement
and requested that he view a photographic array that
included one photograph of the petitioner. Clement was
immediately drawn to one photograph but did not want
to be too hasty in making an identification. Id. Initially,
he eliminated all but two photographs as possibilities
but kept returning to one photograph, that of the peti-
tioner, that had initially attracted his attention. Id. Clem-
ent stated that his identification was based primarily
on his recognition of the petitioner’s eyes, which were
the same eyes as the gunman. Id., 130–31.
   On the basis of Valle’s and Clement’s identifications,
the police obtained an arrest warrant for the petitioner,
and executed it several days later. Id., 131. The state
filed a five count information charging the petitioner
with one count of felony murder, three counts of rob-
bery in the first degree, and one count of attempt to
commit robbery in the first degree. Id.
                             B
  The following additional evidence presented at the
petitioner’s criminal trial is relevant to this appeal. As
recounted previously, at trial, the state presented testi-
mony from two of the robbery victims, Valle and Clem-
ent, who described the events of the night of the robbery
and the murder of Delgado. Both Valle and Clement
identified the petitioner as the person who entered with
the gun.
  In light of these identifications, the petitioner was
arrested. He subsequently gave a statement to the
police, blaming the murder on Soler. Soler’s photograph
was placed in a photographic array and shown to Valle,
who identified Soler as the person who had assisted
the gunman during the course of the robbery. Soler
was arrested and charged with the same offenses as
the petitioner.
  The state called Soler to testify at the petitioner’s
criminal trial. Soler’s account of the incident in question
was largely similar to Valle’s and Clement’s testimony
describing the incident, and Soler testified that the peti-
tioner was the gunman. He also testified that during a
chance encounter at the prison medical unit, the peti-
tioner asked Soler to recant the statement he had
already given to the police about the incident. Soler
also testified that the petitioner questioned him about
whether he would testify against the petitioner at his
trial.
   On direct examination, the prosecutor asked Soler if
he had been promised any benefits from the state in
exchange for his testimony, which Soler denied. When
prodded on cross-examination about his motivation for
testifying, Soler stated: ‘‘I’m testifying cuz it’s the right
thing to do.’’ Soler further stated that he was not offered
any particular deal by the state and that he did not know
whether he would receive any kind of consideration as
a result of testifying. Soler also testified that he would
not lie about the events of the night in question in order
to benefit himself.
   Following Soler’s testimony, and outside the pres-
ence of Soler and the jury, defense counsel requested
that the court inquire of the state, on the record, if
there were any discussions relayed to Soler about his
cooperation being brought to his sentencing court’s
attention. Specifically, defense counsel questioned
whether Soler was told that the felony murder charge
would be dropped if he were to testify in accordance
with the facts that existed.
   In response, the prosecutor explained that, because
Soler testified at trial, ‘‘some credit perhaps would be
due him. What the extent of that credit is, I don’t know.
I know counsel has suggested that perhaps I would
reduce the charge. We’ve had discussions that maybe
that would happen. I can’t say that it would. In my
discussions with [Soler], I’ve indicated to him that I
hadn’t made any promises to him, so we have not come
to a disposition or an understanding as to what any
testimony would be. . . . [His testimony] potentially
ultimately would be presented to a sentencing judge
. . . . I don’t see how that would not happen.’’
   The court responded by stating that ‘‘some favorable
consideration is something that [the state] would cer-
tainly consider at some point in time, but no promises
have been made.’’ The prosecutor replied, ‘‘[r]ight.’’ The
prosecutor further explained that ‘‘[the petitioner] was
deciding to elect trial, so essentially for [Soler], we sort
of tabled his case because he was available and willing
to participate in [the petitioner’s] trial.’’ When defense
counsel questioned whether Soler’s testimony would
mean that ‘‘his charges could be lowered and he would
not face a mandatory minimum of twenty-five years,’’
the prosecutor responded by stating that, ‘‘I’ve not con-
veyed that to him . . . my conversations with him were
that there are no offers on the table. . . . [H]ow this
works out is still yet to be determined.’’
   Soler’s defense attorney then stated: ‘‘We have dis-
cussed the possibility of there being a benefit. We had at
one point, I believe, discussed the possibility of coming
down to twenty-five years if a variety of things fell into
place. I do not believe that I’ve ever indicated to my
client that I had received an offer because there has
never been an offer from the state in this case or an
indication from the state that they would be inclined
to drop the charge . . . .’’
   The court summarized: ‘‘[T]here’s been no fixed offer.
And that’s the way it should be characterized . . . . It
doesn’t rise to the level of a promise. It’s not a promise.’’
The prosecutor affirmed her understanding that, if ben-
efits had been offered in exchange for testimony, the
state would have been obligated to disclose such infor-
mation. The court, therefore, accepted the prosecutor’s
representation that no agreement existed.
   In addition to the testimony of two of the robbery
victims, the state also presented a statement the peti-
tioner had given to the police after his arrest, in which
he blamed the murder on Soler. The statement was read
into the record at trial. In the statement, the petitioner
admitted to the police that he had gone to Delgado’s
apartment on the night of the robbery with Soler, whom
the petitioner referred to by his nickname, ‘‘Monstruo.’’
He claimed that they briefly stopped in at the apartment,
looking to obtain marijuana, which they bought, and,
just as they were about to leave, Soler stopped him
and was holding a gun. According to the petitioner’s
statement, Soler proceeded to rob the victims, at one
point asking the petitioner to hold the gun for him. The
petitioner stated that, after he returned the gun to Soler,
Delgado approached and grabbed Soler, leading to a
struggle during which Delgado was shot. See footnote
4 of this opinion.
   The state also presented testimony at the petitioner’s
criminal trial from an inmate, David Williams, who had
been incarcerated in the same facility as the petitioner
and Soler while they awaited trial. Williams had pre-
viously known both Soler and the petitioner for about
ten years. Williams testified that, while they were incar-
cerated, the petitioner asked Williams if he knew Soler.
When Williams confirmed that he knew Soler, the peti-
tioner informed Williams that Soler was his accomplice
in the incident giving rise to the petitioner’s arrest
and incarceration.
   Williams testified that the petitioner eventually told
him that ‘‘he could help [Williams] with [his] case, [Wil-
liams] could help [the petitioner] with his case . . . .’’
The help that the petitioner sought was for Williams
‘‘to give [the petitioner’s] lawyer a statement . . . that
[Soler] had told [Williams] he had shot somebody . . .
[a]nd that they had somebody else for the murder.’’
   Williams further testified that the petitioner wrote
what he wanted Williams to say in the false confession
in a letter. The petitioner then instructed Williams to
convey the details of the letter to his attorney, who
would then get in touch with the petitioner’s attorney
or investigator. Williams testified that the petitioner
‘‘said to memorize it and rip it up when I finish memoriz-
ing,’’ before speaking to his attorney. Instead, Williams
gave the letter to his attorney and told him how he had
received it.1
  Williams testified that the petitioner was urging him
to claim that this was a conversation between Williams
and Soler while they were on the same cellblock, even
though Williams and Soler were actually on the cell-
block together for only ‘‘a couple hours’’ total, and did
not speak to each other in that time. Williams testified
that the petitioner admitted to Williams that he was
actually the person who ‘‘shot the kid’’ that night.
                            C
   The petitioner’s defense counsel presented the
defense case by cross-examining the state’s witnesses
to cast doubt on the validity of their testimony. They
did not present any witnesses for the defense. Defense
counsel argued to the jury in closing that the victims
who had identified the petitioner likely chose the peti-
tioner’s photograph from the array because his photo-
graph, which was the only one with a white ruler and
bright lighting, stood out from other photographs pre-
sented to the victims. Defense counsel also asserted
that the petitioner’s statement to the police was not
reliable because he was pressed into giving a statement
when the police confronted him with the prior, allegedly
tainted identifications by the victims. See footnotes 4
and 5 of this opinion. As for Soler, defense counsel
specifically argued that he was likely looking for a deal
in exchange for his testimony, telling the jury that Soler
was involved and has ‘‘been around the block, he has
a lot to lose, and he knows that what he could do is
he can get off felony murder, not get the twenty-five
year mandatory minimum if he comes in here and he
says what the state wants him to say and, anyway,
he can say it.’’ Defense counsel discredited Williams’
testimony as a fabrication by someone facing a man-
slaughter charge and looking for a deal, and pointed
out that Soler and Williams knew each other before
they were incarcerated, thereby implying that they
might have worked together to pin the crime on the
petitioner. Lastly, defense counsel critiqued the ability
of the victims to recall certain events during the robbery
and the thoroughness of the police investigation.
                            D
  At the conclusion of the trial, the jury found the
petitioner guilty of one count of felony murder in viola-
tion of General Statutes § 53a-54c, two counts of rob-
bery in the first degree in violation of General Statutes
§ 53a-134 (a) (2), and one count of attempt to commit
robbery in the first degree in violation of § 53a-134 (a)
(2) and General Statutes § 53a-49.2 State v. Marquez,
supra, 291 Conn. 124. The court rendered judgment in
accordance with the verdict and sentenced the peti-
tioner to a term of fifty years imprisonment, execution
suspended after thirty-five years, and five years of pro-
bation.
  On direct appeal to this court, the petitioner claimed
that the trial court improperly denied his motion to
suppress two eyewitness identifications, which violated
his right to due process of law under both the state and
federal constitutions. Id. We affirmed the trial court’s
judgment. Id., 167.
                             E
   The petitioner then filed a petition for a writ of habeas
corpus, claiming a violation of his due process rights
because of the state’s failure to disclose material, excul-
patory evidence in his underlying criminal trial. Specifi-
cally, the petitioner claimed that the state had an
undisclosed agreement with Soler that his charges
would be reduced in his pending criminal matter in
exchange for testimony against the petitioner. He also
claimed that the prosecutor knowingly failed to correct
Soler’s false testimony that he had received no consider-
ation in exchange for his cooperation. If the state had
made the appropriate disclosure and correction, the
petitioner asserted, the result of his trial would have
been different and more favorable to him.
   These assertions are based in large part on informa-
tion exposed during Soler’s sentencing. At that time,
the prosecutor stated that ‘‘the state had represented to
[Soler’s] counsel that, in the event that [the petitioner]
chose to proceed to trial and that [Soler’s] testimony
would be needed and would, in fact, be forthcoming
and be proffered truthfully . . . the state would sort of
come off the felony murder [charge] and charge various
counts of robbery or some of the substantive offenses
in lieu of the felony murder since that would have a
minimum mandatory of twenty-five years to serve. And
that was discussed with the victim’s family and other
victims as well.’’ (Emphasis added.) Notably, after Soler
testified at the petitioner’s trial, the prosecution chose
not to pursue the felony murder charge originally
brought against him. Instead, he was sentenced to a
total term of twenty years of imprisonment, execution
suspended after nine years, and five years of probation,
for two counts of robbery in the first degree and attempt
to commit robbery in the first degree.
   Notwithstanding the phrasing he used at sentencing,
at the petitioner’s habeas trial, Soler’s prosecuting attor-
ney testified that his statement at Soler’s sentencing
‘‘was referring to discussions subsequent to his testi-
mony, not prior to’’ it. He also stated that the discussion
he probably was referring to was when he ‘‘discussed
with the [victim’s] family whether or not they would
object to [Soler] having the charge other than felony
murder . . . .’’ He also stated that ‘‘[w]e didn’t codify
or create any deals. . . . So if I did discuss or say or
suggest things while [Soler’s] case was pending, it
would be in sort of the hypothetical that maybe we
could do things.’’ He insisted that, ‘‘at that time that
[Soler] testified, I made no offers . . . .’’
   The prosecutor further explained that his decision
not to pursue the felony murder charge was, instead,
‘‘based upon [Soler’s] cooperation, based upon his com-
pleteness and truthfulness in his statement from day
one when he got arrested,’’ and because ‘‘felony murder
. . . carries a mandatory twenty-five year sentence. I
didn’t think that was an appropriate sentence for his
role,’’ given that he was not the gunman. He also testi-
fied that, as a general policy in all criminal matters, he
does not ‘‘make a deal [with any cooperating witness]
because it doesn’t pay as a prosecutor to try to make
a deal upfront because you don’t know how it’s going
to work out’’ with the quality of the witness’ testimony.
   The habeas court denied the petitioner’s habeas peti-
tion, concluding that none of the testifying witnesses
in the petitioner’s underlying criminal trial had
agreements promising them benefits in exchange for
their testimony, and, thus, no Brady violation occurred.
The petitioner sought certification to appeal from the
judgment, claiming that, among other things, the habeas
court made a clearly erroneous factual finding that there
was no agreement between the state and Soler at the
time of his testimony in the petitioner’s underlying crim-
inal trial. The habeas court denied the petition for certi-
fication to appeal. The petitioner then appealed to the
Appellate Court, which dismissed the petitioner’s
appeal, concluding that the habeas court did not abuse
its discretion in denying the petition for certification
to appeal. Marquez v. Commissioner of Correction,
supra, 170 Conn. App. 240–41.
   We granted the petitioner’s petition for certification
to appeal, limited to the following issues: First, ‘‘[d]id
the Appellate Court properly conclude that the habeas
court did not abuse its discretion in denying the petition-
er’s petition for certification to appeal?’’ Second, ‘‘[i]f
not, did the habeas court properly find that the state did
not fail to disclose, in violation of Brady v. Maryland,
[supra, 373 U.S. 87], and its progeny, material impeach-
ment evidence concerning plea discussions between
the state and a key state’s witness?’’ Marquez v. Com-
missioner of Correction, 324 Conn. 925, 925–26, 155
A.3d 1269 (2017).
                            II
   The petitioner argues that the state created an infor-
mal leniency agreement with Soler, conveying to him
that, in exchange for testimony favorable to the state,
he would receive a lesser charge. The petitioner argues
that this undisclosed agreement violates Brady and its
progeny, as did the state’s failure to correct Soler’s
false testimony that no such agreement existed. The
petitioner also asks us to conclude that the nondisclo-
sure of Soler’s agreement and his uncorrected false
testimony were material under the Brady doctrine.
Brady v. Maryland, supra, 373 U.S. 87. The respondent,
the Commissioner of Correction, argues that, although
plea discussions took place, no agreement was ulti-
mately formalized and, thus, no Brady violations took
place. The respondent further argues that Soler’s testi-
mony was immaterial. We agree that, under due process
standards, Soler’s testimony was immaterial, and, there-
fore, we have no occasion to reach the question of
whether an agreement was formed between Soler and
the state.
                             A
   Before turning to the merits of the case, we must
first address the habeas court’s decision to deny the
petitioner’s petition for certification to appeal. General
Statutes § 52-470 (g) provides in relevant part that ‘‘[n]o
appeal from the judgment rendered in a habeas corpus
proceeding . . . may be taken unless the appellant
. . . petitions the judge before whom the case was tried
. . . to certify that a question is involved in the decision
which ought to be reviewed by the court having jurisdic-
tion and the judge so certifies.’’ This statute ‘‘prevents
a reviewing court from hearing the merits of a habeas
appeal following the denial of certification to appeal
unless the petitioner establishes that the denial . . .
constituted an abuse of discretion by the habeas court.’’
Kaddah v. Commissioner of Correction, 299 Conn. 129,
135, 7 A.3d 911 (2010). In the present case, the habeas
court found that no arrangement existed between the
state and Soler that had to be disclosed to the defense
and declined to find that the question merited review
by an appellate court.
   Ordinarily, a petitioner must overcome the denial of
certification to appeal by proving that the habeas court
abused its discretion on the basis of one of three factors.
Id., 136. We previously have concluded, however, that
‘‘we need not decide whether the habeas court abused
its discretion in denying certification to appeal’’ when
there is ‘‘an alternat[ive] ground for affirming the deci-
sion of the habeas court’’ and the petitioner, therefore,
‘‘cannot obtain the relief he requested in the present
petition,’’ even if he were to prevail on the question
addressed by the habeas court. Id., 136. In the present
case, because the petitioner’s claim fails on the basis
of materiality, regardless of whether the habeas court
properly denied certification on the question of whether
there was an agreement, we do not address the habeas
court’s decision to deny certification. We instead affirm
on that alternative basis.3
                            B
   We begin our analysis with an overview of the princi-
ples that govern a claim that the state failed to disclose
an agreement with a cooperating witness in exchange
for the witness’ testimony. The fourteenth amendment
to the United States constitution demands that ‘‘[n]o
State shall . . . deprive any person of life, liberty, or
property, without due process of law . . . .’’ U.S.
Const., amend. XIV, § 1. Due process principles require
the prosecution to disclose to the defense evidence that
is favorable to the defendant and material to his guilt
or punishment. Brady v. Maryland, supra, 373 U.S. 87;
see also State v. Ortiz, 280 Conn. 686, 717, 911 A.2d
1055 (2006). In order to obtain a new trial for improper
suppression of evidence, the petitioner must establish
three essential components: (1) that the evidence was
favorable to the accused; (2) that the evidence was
suppressed by the state—either inadvertently or wil-
fully; and (3) that the evidence was material to the case,
i.e., that the accused was prejudiced by the lack of
disclosure. See, e.g., State v. Ouellette, 295 Conn. 173,
185, 989 A.2d 1048 (2010).
   The state’s failure to disclose an agreement with a
cooperating witness may be deemed to be the withhold-
ing of exculpatory evidence. Impeachment evidence
‘‘falls within Brady’s definition of evidence favorable
to an accused.’’ (Internal quotation marks omitted.) Id.
Impeachment evidence is ‘‘broadly defined’’ in this con-
text as evidence that could potentially alter the jury’s
assessment of a witness’ credibility. (Internal quotation
marks omitted.) State v. Jordan, 314 Conn. 354, 370,
102 A.3d 1 (2014). Specifically, we have noted that ‘‘[a]
plea agreement between the state and a key witness is
impeachment evidence falling within the . . . Brady’’
doctrine. (Internal quotation marks omitted.) State v.
Ouellette, supra, 295 Conn. 185. An undisclosed
agreement for benefits between Soler and the state falls
within the broad definition of impeachment evidence.
   In addition to alleging failure to disclose an
agreement, the petitioner also argues that an additional
due process violation occurred when the state failed
to correct Soler’s alleged false testimony at trial regard-
ing the absence of an agreement. We have explained
that ‘‘[d]ue process is . . . offended if the state,
although not soliciting false evidence, allows it to go
uncorrected when it appears.’’ (Internal quotation
marks omitted.) Id., 186; see also Napue v. Illinois,
supra, 360 U.S. 269. Even if the denial of a leniency
agreement is not outright false, but only ‘‘substantially
mischaracterizes’’ the nature of the agreement, we have
indicated that ‘‘the state is obliged to correct the mis-
conception.’’ (Internal quotation marks omitted.) State
v. Ouellette, supra, 295 Conn. 186; see also Giglio v.
United States, supra, 405 U.S. 153; Napue v. Illinois,
supra, 269–70.
  For the purposes of our analysis, we will assume,
without deciding, that the state improperly failed to
disclose impeachment evidence concerning the alleged
agreement it reached with Soler. We therefore turn to
consider whether the lack of any disclosure of such an
agreement to the defense and the failure to correct
Soler’s testimony that no such agreement existed
were material.
   We begin by noting that determining materiality pre-
sents a question of law subject to plenary review. See,
e.g., State v. Ortiz, supra, 280 Conn. 720; see also Jones
v. State, 328 Conn. 84, 102–103, 177 A.3d 534 (2018).
   Evidence is material when there ‘‘would be a reason-
able probability of a different result’’ if it were disclosed.
(Internal quotation marks omitted.) State v. Jordan,
supra, 314 Conn. 370. A reasonable probability exists
if the evidence ‘‘could reasonably . . . put the whole
case in such a different light as to undermine confidence
in the verdict.’’ (Internal quotation marks omitted.)
State v. Ortiz, supra, 280 Conn. 717. Materiality does
not require, however, a ‘‘demonstration . . . that dis-
closure of the suppressed evidence would have resulted
ultimately in the defendant’s acquittal.’’ (Internal quota-
tion marks omitted.) Id., 717–18. Instead, the operative
inquiry is whether, in the absence of the evidence, the
defendant ‘‘received a fair trial . . . resulting in a ver-
dict worthy of confidence.’’ (Internal quotation marks
omitted.) Id., 718.
   In the context of a false testimony Brady violation,
the standard for materiality is ‘‘significantly more favor-
able to the defendant’’ than it is with other forms of
exculpatory evidence. (Internal quotation marks omit-
ted.) State v. Jordan, supra, 314 Conn. 370. A conviction
obtained through uncorrected false testimony ‘‘must be
set aside if there is any reasonable likelihood that the
false testimony could have affected the judgment of the
jury.’’ (Internal quotation marks omitted.) Id., 370–71.
In other words, ‘‘reversal is virtually automatic . . .
unless the state’s case is so overwhelming that there
is no reasonable likelihood that the false testimony
could have affected the judgment of the jury.’’ (Empha-
sis in original; internal quotation marks omitted.) Id.,
371.
   This calls for ‘‘a careful review of that testimony and
its probable effect on the jury, weighed against the
strength of the state’s case and the extent to which
[the defendant was] otherwise able to impeach [the
witness].’’ (Internal quotation marks omitted.) Id.
‘‘[E]vidence that may first appear to be quite compelling
when considered alone can lose its potency when
weighed and measured with all the other evidence, both
inculpatory and exculpatory. Implicit in the standard
of materiality is the notion that the significance of any
particular bit of evidence can only be determined by
comparison to the rest.’’ (Internal quotation marks omit-
ted.) State v. Wilcox, 254 Conn. 441, 455, 758 A.2d 824
(2000). To aid in this comparison, a court may take
judicial notice of the underlying criminal trial tran-
scripts during the petition hearing or on appeal. See,
e.g., Andrades v. Commissioner of Correction, 81
Conn. App. 538, 540, 840 A.2d 1198 (2004).
                              C
   Applying these principles to the present case, we
must consider Soler’s alleged false testimony that he
was testifying solely ‘‘cuz it’s the right thing to do,’’ that
the prosecutor ‘‘didn’t’’ offer him a plea deal, and that
he did not expect to get any consideration for his testi-
mony in comparison to all of the other evidence pre-
sented at the criminal trial. The petitioner claims that,
if the jury had known that, in exchange for his testi-
mony, ‘‘the state would sort of come off the felony
murder’’ charge, there is a reasonable likelihood that the
jury would have seen the case differently. We conclude,
however, that there is no reasonable likelihood that full
disclosure of any agreement or Soler’s allegedly false
testimony would have brought about a different result
at trial.
   First, it is important to point out that, at his criminal
trial, there was little question that the petitioner was
present at the scene. The state presented a statement
given by the petitioner to the police acknowledging
that he was present during the incident that caused
Delgado’s death, and that he had, at some point, held
the gun used in the murder.4 The primary issue in the
case, if the petitioner’s statement is credited,5 therefore,
was whether the petitioner participated in the robbery
that led to Delgado’s murder.6
   There was ample evidence presented at trial to show
not only that the petitioner actively participated in the
robbery, but that he also fired the shots that killed
Delgado. Valle clearly identified the petitioner to be the
gunman. He testified that he first observed the peti-
tioner in a ‘‘brightly lit’’ hallway. Then, after entering
the apartment, the petitioner was only ‘‘[i]nches’’ away
from Valle’s face. Even though the living room was
unlit, Valle stated that he ‘‘could see [the petitioner]
real good’’ because of the light pouring in from other
rooms. When speaking to the police, Valle was able to
give a detailed description of the petitioner, including
his approximate height, hairstyle, hair length, build,
approximate age, and complexion. Additionally, Valle
noted that, when he first saw the petitioner at the apart-
ment, he thought that the petitioner ‘‘exactly’’ resem-
bled someone else that Valle knows. Valle specifically
told the police at the time of the murder that his observa-
tion of the petitioner and Soler would allow him to
identify the two men if given the chance.
   Although two men came into the apartment looking to
rob the occupants, the man that Valle positively identi-
fied as the petitioner was the same man who, he testified,
displayed the gun when he came into the apartment,
directed Valle and the others to sit on the couch, and
indicated that his gun was ‘‘on safety.’’ The other individ-
ual ‘‘acted like he had [a gun], but he never showed it.’’
It was the petitioner whom Valle described as struggl-
ing with Delgado when the gun went off.
   When Valle saw the petitioner again at the parole
office—out of context from any investigation or
prompting—Valle immediately recognized him. When
subsequently presented with a photographic array, ‘‘[i]t
only took [Valle] three seconds’’ to identify the peti-
tioner as ‘‘the one [who] had the gun.’’ In response to
a question from the prosecutor as to how certain he
was of his identification of the petitioner as the mur-
derer, Valle replied, ‘‘I’m positive.’’ Simply put, Valle
provided strong evidence of the petitioner’s guilt by
identifying him during a chance encounter, selecting
with certainty his photograph from an array, identifying
him in court, and providing credible, corroborated testi-
mony about the incident in question.
   Clement provided testimony consistent with Valle’s
testimony. Clement confirmed that, on the night of the
murder, ‘‘[i]t was light . . . enough to see’’ in the living
room, as light was provided by adjoining rooms that
did not have doors. Clement came within ‘‘[a] foot or
two’’ of the robbers, and handed the petitioner his
watch, providing him ample opportunity to observe the
petitioner and Soler. Clement told the responding police
officers, ‘‘I could give you a good description of what
[the petitioner and Soler look] like, and if you were to
catch them, I could point them out. . . . More with the
guy with the gun. . . . [T]he guy with the gun, I could—
I remembered his clothes pretty good. . . . And his
eyes I could probably catch if I saw him again.’’ Clement
testified that he had the presence of mind during the
robbery to make a concerted effort to remember the
gunman’s appearance because, based on a prior experi-
ence, he knew that he might have to identify the perpe-
trator. He noted: ‘‘I was enough minded to at least to
be able to look the guy in his eyes.’’
   Upon viewing the photographic array, Clement stated
that, ‘‘right away, there was one photograph that caught
my attention. . . . And then I paused for a second and
I wanted to look at the other ones because I didn’t
want to just give [the detective] an answer right away.
I wanted to make sure I got it right. . . . And I looked
at another guy . . . briefly, but then I eventually went
back to my first instinct.’’ In response to a question
from the prosecutor as to how certain Clement was
of his identification of the petitioner as the murderer,
Clement testified, ‘‘I was pretty sure, 90 percent.’’ Clem-
ent stated that what made him certain about the identifi-
cation was the petitioner’s ‘‘eyes. . . . [I]t’s more his
eyes and pretty much his facial features. I could pretty
much tell.’’ Clement’s memory of the petitioner’s facial
features lends credibility to his identification, as
opposed to reliance on a changeable feature, such as
the petitioner’s facial hair. At the end of his testimony,
Clement made an in-court identification of the peti-
tioner as the person who was carrying the gun during
the robbery.
   In short, both Valle and Clement presented persua-
sive testimony, selecting with confidence the petition-
er’s photograph from a photographic array, identifying
him in court, and providing testimony consistent with
one another’s accounts of the evening.
  In addition to Valle’s and Clement’s strong testimony,
the state provided confession and consciousness of
guilt evidence. The petitioner’s fellow inmate, Williams,
testified that the petitioner had confessed to him that
he was the one who shot Delgado that night. Williams
testified that the petitioner stated that he used an ‘‘old
black Colt .45’’ gun and shot Delgado in the neck while
Soler ran away.
   Additionally, consciousness of guilt evidence was
presented at trial through Williams’ testimony that the
petitioner sought to trade favors with him by suggesting
that each testify falsely at each other’s trials. Williams
testified that the petitioner wrote him a letter containing
a false story, reversing Soler’s and the petitioner’s roles,
with Soler confessing to the murder to Williams in jail.
The petitioner instructed Williams to communicate the
letter’s contents to his own attorney, who would convey
it to the petitioner’s attorney and then destroy it. The
letter, however, was entered into evidence and con-
tained details largely corroborating Soler’s testimony,
save for the role reversal. See footnote 1 of this opinion.
   Soler’s testimony served only to corroborate indepen-
dent testimony from eyewitnesses Valle and Clement,
testimony from Williams, who heard a direct confession
from the petitioner himself, and the petitioner’s written
confession attempting to frame Soler as the gunman.
Soler provided very little information about the incident
that was not also revealed by Valle, Clement, Williams,
and by the petitioner’s own written words, rendering
much of Soler’s testimony duplicative.
  Moreover, Soler was thoroughly impeached on cross-
examination. Although he did not admit to receiving
any benefit, he did admit that he was hoping his attorney
could do ‘‘[w]hatever she can do’’ to make him a good
deal on the felony murder charge. Soler also testified
that he did not speak to the police until after he was
arrested because he was hoping to get away with the
crimes. In other words, he conceded opportunistic aspi-
rations for the disposition of his own case, regardless
of whether a formal deal existed. Throughout cross-
examination, defense counsel continually focused on
Soler’s motivation to testify consistently with the state’s
narrative of the case. In fact, Soler admitted that it
was only after he was arrested that he was willing to
cooperate. Defense counsel also impeached Soler in
other ways, underscoring Soler’s drug use, voluntary
participation in the underlying armed robbery, and the
fact that his nickname on the streets is Monstruo—the
Spanish word for ‘‘monster.’’ Defense counsel told the
jury, during closing arguments, that Soler likely testified
as a means to have the felony murder charge, and its
mandatory minimum sentence, dropped in exchange
for testimony favorable to the state.
   Thus, even if jurors believed Soler’s allegedly false
testimony that he did not have a deal with the prosecu-
tor, their impression was harmful only to the extent
that Soler’s testimony provided unique value to the
state’s case. Given the testimony of Valle, Clement, Wil-
liams, and the handwritten confession evidence, we are
not persuaded that Soler’s testimony proved significant
aside from its consistency with multiple other wit-
nesses. When Soler’s testimony is weighed against the
overwhelming strength of the state’s case, as we are
obligated to do, the elevated standard for materiality
is not met.
  In support of his materiality claim, the petitioner prin-
cipally asserts that ‘‘it is likely that Soler’s testimony
was extremely influential on the jury,’’ and, thus, Soler’s
hidden motives were ‘‘not harmless.’’ He supports this
contention by emphasizing that there were ‘‘problems
surrounding the state’s other witnesses.’’ We find these
problems to be largely illusory.
   Most notably, the petitioner contends that ‘‘the tenu-
ous credibility of the testimony of Clement, Valle and
Williams,’’ was ‘‘insufficient to render Soler’s false testi-
mony harmless . . . .’’ Specifically, the petitioner con-
tends that Clement ‘‘felt that he ‘had to pick somebody’ ’’
in the photographic array and was ‘‘vacillating between
two individuals in the lineup.’’ This is an incomplete
representation of Clement’s testimony. Clement testi-
fied that he ‘‘was pretty sure, 90 percent’’ confident in
his identification of the petitioner as the gunman. He
also testified that he intentionally hesitated in making
his identification out of an abundance of caution
because he ‘‘wanted to make sure [he] got it right.’’ He
also provided detailed testimony about his memory of
the petitioner’s facial features, which he purposely stud-
ied at the time of the incident because he had the pres-
ence of mind to know that he may have to identify the
gunman in the future. Moreover, he testified that the
officers who presented the photographic array to him
‘‘didn’t make it sound like’’ he ‘‘had to pick somebody.’’
(Emphasis added.)
  The petitioner also asserts that Valle was a weak
witness because he ‘‘was consuming alcohol on the
evening of the homicide’’ and ‘‘did not even witness the
fatal shot that was fired . . . .’’ He also emphasizes
that ‘‘Valle was serving a sentence in a criminal matter
and had not been abiding by the conditions of his ‘addic-
tion program.’ ’’ These qualifications, while true, are
unpersuasive in discrediting Valle’s testimony.
   Although Valle was consuming alcohol that night, he
characterized his consumption as drinking ‘‘a little bit’’
and noted that the alcohol he purchased was shared
among four individuals. Notably, there was no testi-
mony presented by either Valle or Clement that they
were drunk or had consumed excessive amounts of
alcohol that evening. At best, the extent to which Valle’s
alcohol consumption weakens or impairs his testimony
is unclear.
  The petitioner’s argument that Valle did not observe
the fatal shot being fired is unconvincing. Although he
had fled to another room by that time, Valle still had
the opportunity to ‘‘see [the petitioner] real good’’ and
was ‘‘positive’’ when he identified the petitioner as the
gunman in a photographic array. Although Valle did not
know with eyewitness certainty that the petitioner was
the one who fired the fatal shot, he did witness the
petitioner as the only one with a visible gun and
observed that Delgado had begun physically fighting
with the armed petitioner immediately before Valle
exited the living room and the gun discharged.
   And, although it is true that Valle was serving a sen-
tence in a criminal matter and was participating unsuc-
cessfully in an addiction program, these facts do not
discredit his testimony. On redirect examination, the
prosecutor underscored the fact that, in Valle’s pending
case, he did not use his cooperation in the present case
to gain any benefit for the disposition of his own case.
As for the noncompliance with his addiction program,
in the absence of any additional facts, we see no reason
why it would discredit his testimony in any meaning-
ful way.
    Finally, the petitioner discounts Williams’ testimony
on the basis of his admission ‘‘that he had an interest
in testifying for the state and an expectation of a benefit
. . . .’’ Although Williams was somewhat of a ‘‘jailhouse
snitch,’’ he did testify that it was the petitioner who, in
fact, sought him out for help in framing Soler as the
gunman. The prosecutor fully exposed Williams’ self-
interest, appropriately leaving it to the jury to weigh
his credibility. Notwithstanding Williams’ status as a
‘‘jailhouse snitch,’’ the bottom line remains that his testi-
mony concerning the petitioner’s story about the events
that night was consistent with the other witnesses’
accounts. More important, Williams provided the letter
as physical evidence corroborating the petitioner’s
attempt to engineer false testimony to frame Soler as
the shooter. Biased or not, Williams’ value as a witness
stems from his possession of the physical evidence
exposing the petitioner’s plot to blame his accomplice,
demonstrating powerful consciousness of guilt evi-
dence that no level of self-interest could negate.
  Because we do not find the testimony of Clement,
Valle, and Williams ‘‘problematic,’’ as the petitioner
urges, we disagree that ‘‘[e]xposing Soler’s motives
would have significantly detracted from the [jury’s]
crediting’’ the testimony of the other witnesses. Given
how strong the state’s case was, exposing Soler’s
motives would not have made a meaningful difference.
  In the present case, ‘‘the state’s case [was] so over-
whelming that there is no reasonable likelihood that
[Soler’s] false testimony could have affected the judg-
ment of the jury.’’ (Emphasis omitted; internal quotation
marks omitted.) State v. Jordan, supra, 314 Conn. 371.
After weighing Soler’s testimony, its probable effect on
the jury, the strength of the state’s case, and the extent
to which defense counsel was able to impeach Soler,
we conclude that Soler’s allegedly false testimony and
the prosecutor’s failure to correct it were immaterial
under Brady. See id.
                           III
   The petitioner also urges us to exercise our supervi-
sory authority ‘‘to require that the state disclose any
representation by a state’s attorney, made to a cooperat-
ing witness, or [his] attorney, concerning the potential
ultimate disposition of [the witness’] pending criminal
case prior to testifying.’’ Although we decline the peti-
tioner’s request in this particular case, we are con-
strained to comment on the state’s practice of informal,
off-the-record leniency understandings with cooperat-
ing witnesses.
   These understandings, like the one in the present
case, often involve a prosecutor’s suggesting—although
not promising—that a favorable recommendation to
the sentencing judge and/or a reduction in the charges
against the witness might be forthcoming in exchange
for the witness’ testimony inculpating another defen-
dant. See, e.g., Adams v. Commissioner of Correction,
309 Conn. 359, 363, 71 A.3d 512 (2013); Hines v. Com-
missioner of Correction, 164 Conn. App. 712, 717–23,
138 A.3d 430 (2016). Often such representations are
made only to the witness’ counsel, while the prosecu-
tor’s communication with the witness makes clear that
there is no promise. Under such circumstances, the
prosecutor may not actually know if any representa-
tions of possible leniency have been conveyed by the
witness’ counsel to the witness. Thereafter, if, before
the jury, the witness denies that there is any actual
‘‘agreement’’ or ‘‘deal,’’ the prosecutor can accurately
state, as the respondent argues in this case, that he
does not have a reason to know if the witness is being
untruthful. Although it might very well be accurate that
no definitive promises have been made by the state,
and, even if any possible outcomes as described to
counsel might be ‘‘tentative,’’ experienced counsel
operating in a courthouse in which he or she is familiar
with the practices of prosecutors and presiding judges
can comfortably advise the witness of the possible
credit that might follow from his testimony. Thus, these
‘‘hypothetical’’ outcomes serve as a real incentive to
motivate a witness to testify for the state.
   Left out of this equation, however, is the jury. See
Adams v. Commissioner of Correction, supra, 309
Conn. 369–73 (collateral review of conviction obtained
by false testimony requires ‘‘a careful review of that
testimony and its probable effect on the jury’’). These
vague understandings can prevent defense counsel
from effectively impeaching the witness for bias, per-
haps leaving jurors ‘‘with the impression . . . that [the
witness did not have] any incentive to testify favorably
for the state.’’ State v. Jordan, 135 Conn. App. 635, 667,
42 A.3d 457 (2012), rev’d in part on other grounds by
State v. Jordan, 314 Conn. 354, 102 A.3d 1 (2014). Jurors
are not well versed in the nuanced vagaries of such
leniency agreements. Yet, we rely on jurors to assess
a witness’ credibility—including a witness’ motivation
to testify—while withholding from them critical infor-
mation that would help them assess just how motivated
that witness might be. This practice, therefore, carries
with it risks that threaten the efficient and fair adminis-
tration of justice.
    First, and most obvious, a defendant’s constitutional
rights may be violated if information about a potential
plea agreement likely to bear on a witness’ motivation
to testify is not disclosed. As a result, a court in a later
collateral proceeding might indeed conclude that the
state’s disclosure of its pretrial understandings was
insufficient under Giglio v. United States, supra, 405
U.S. 153, Brady v. Maryland, supra, 373 U.S. 87, and
Napue v. Illinois, supra, 360 U.S. 269. See, e.g., Adams v.
Commissioner of Corrections, supra, 309 Conn. 363–64,
365 n.11 (although prosecutors intentionally created
‘‘firewall’’ so they would not know what promises were
given to cooperating witness, state had duty to disclose
witness’ plea agreement). Even if the failure to disclose
is ultimately found not to be material, the practice of
vague understandings can lead to lengthy posttrial
inquiries, delaying finality and consuming resources.
For example, in the present case, the habeas court was
faced with reconstructing and examining, years after
the fact, communications that took place—both on the
record and off-the-record—during a cooperating wit-
ness’ pretrial plea negotiations, during that witness’ tes-
timony at the trial of his accomplice, or during the
witness’ ultimate sentencing hearing. This collateral
fact-finding might include, as in the present case,
attempts to secure testimony from prosecuting authori-
ties or the cooperating witness’ counsel. Issues of privi-
lege, availability, and faulty memories are likely to
abound.
   Second, the absence of an express agreement may
require a defendant to explore other means to reveal
to the jury a cooperating witness’ motivation to testify.
For example, in an attempt to inform the jury about a
system in which promises are not explicitly made but
understandings are drawn from pretrial discussions,
defendants might resort to calling expert witnesses to
attempt to explain to the jury just how much leniency
a cooperating witness can expect from his testimony.
See, e.g., Servello v. Commissioner of Correction, 95
Conn. App. 753, 763, 899 A.2d 636 (petitioner claimed
that his defense counsel should have called expert wit-
ness at trial to testify whether informant ‘‘expected
to receive, or already had received, consideration in
exchange for his cooperation’’), cert. denied, 280 Conn.
904, 907 A.2d 91 (2006); see also United States v. Noze,
255 F. Supp. 3d 352, 353 (D. Conn. 2017) (defendant
sought to offer expert testimony about ‘‘ ‘the incentives
and the benefits cooperating witnesses receive for testi-
fying’ ’’); State v. DuBray, 317 Mont. 377, 389–90, 77
P.3d 247 (2003) (defendant sought to present expert
testimony regarding possible benefits that incarcerated
inmate may receive for favorable testimony). This
approach has its own disadvantages. In addition to
increased costs, it leaves the jury to choose between
competing experts without a framework from which to
properly assess the significance of those experts’
opinions.
  Finally, this court or the Rules Committee of the
Superior Court could also conclude that this practice
should be addressed by the exercise of supervisory
authority or the passage of a rule of practice. For exam-
ple, in federal courts, ‘‘it is standard practice in federal
criminal cases for the prosecution to enter into a written
cooperation agreement that memorializes the potential
benefits that may ensue as a result of a cooperating
[witness’] testimony.’’ United States v. Noze, supra, 255
F. Supp. 3d 354. The agreements usually contain an
express provision that the government is not making
any promises as to the level of leniency and that the
recommendation for a reduction in the sentence will
be based on the level of cooperation provided. Cf. U.S.
Sentencing Guidelines Manual § 5K1.1 (2016) (upon
motion of government that defendant has provided sub-
stantial assistance in investigation or prosecution of
another, court may depart from sentencing guidelines).
   Thus, the risks attendant to the practice of entering
into vague, off-the-record, cooperation agreements are
completely avoidable. Understandably, the state is con-
cerned about making actual, enforceable promises to
the cooperating witness because it does not want to
commit to a precise outcome until the witness has testi-
fied. However, outlining the terms of its agreement,
including the charges and the maximum and minimum
exposure to which it has agreed that the witness will
be exposed, does not constrain the state any more than
the practice of entering into an informal understanding
with defense counsel. The state retains the option to
deny the witness an opportunity to plead to a reduced
charge or to receive a lenient sentence if the witness
rescinds the agreement to testify truthfully.
   Finally, the state can avoid the risk that a cooperating
witness will engage in perjury by asking the witness
leading questions about the nature of the witness’
agreement with the state. See Greene v. Commissioner
of Correction, 330 Conn. 1, 27 and n.18, 190 A.3d 851
(2018). Some trial courts find that the better practice
is to make a clear record of the nature of the agreement
or understanding, including the anticipated charge(s)
and the maximum and minimum penalties for those
charges. For example, prior to the witness’ testimony,
on the record but outside the presence of the jury, the
court may ask the prosecutor to outline the nature of the
agreement—the charges and maximum and minimum
penalties—in the presence of the witness, the defen-
dant, and all counsel. Requiring the state to negotiate
the parameters of its cooperation agreement with the
witness ensures the integrity of the process and protects
the state, the witness, and the defendant against the
consequences of an undefined vague agreement. This
approach not only makes a clear record of the
agreement, it eliminates the risk that the disclosure is
insufficient or that the witness will testify untruthfully
about the nature of the agreement and his expectations.
Both sides can examine the witness and argue to the
jury the motivation of the witness to testify and how
that impacts, if at all, the witness’ credibility.
                            IV
   ‘‘We ordinarily invoke our supervisory powers to
enunciate a rule that is not constitutionally required
but that we think is preferable as a matter of policy.’’
(Internal quotation marks omitted.) State v. Medrano,
308 Conn. 604, 630, 65 A.3d 503 (2013). Our supervisory
powers ‘‘are an extraordinary remedy to be invoked
only when circumstances are such that the issue at
hand, while not rising to the level of a constitutional
violation, is nonetheless of utmost seriousness, not only
for the integrity of a particular trial but also for the
perceived fairness of the judicial system as a whole.’’
(Emphasis in original; internal quotation marks omit-
ted.) State v. Hines, 243 Conn. 796, 815, 709 A.2d 522
(1998), quoting State v. Holloway, 209 Conn. 636, 645,
553 A.2d 166, cert. denied, 490 U.S. 1071, 109 S. Ct.
2078, 104 L. Ed. 2d 643 (1989). We decline to invoke
our supervisory authority under these circumstances,
trusting that the above discussion will encourage pru-
dence on the state’s part in its dealings with cooperat-
ing witnesses.
   Because we conclude that, in the present case, the
testimony in question was immaterial under the third
prong of Brady and, therefore, that there was no viola-
tion of the petitioner’s due process rights, we need not
comment further on the state’s disclosure of any pretrial
discussions with Soler. Therefore, we affirm the judg-
ment of the Appellate Court on the alternative basis
of immateriality.
   The judgment of the Appellate Court is affirmed.
  In this opinion McDONALD, ROBINSON and KAHN,
Js., concurred.
   * The listing of justices reflects their seniority status on this court as of
the date of oral argument.
   1
     The letter was entered as a full exhibit during the trial, and Williams
read it in its entirety as part of his testimony. In relevant part, the letter
provided Williams with the following instructions about what to tell his
attorney: ‘‘[Soler] asked if you heard about the kid that got killed on Babcock
back in December . . . . So [Soler] starts telling you that they got somebody
else for the murder, some kid named Julian [the petitioner] . . . . [Soler]
was like oh, we’ll fuck that nigger. That kid [the petitioner] told on [Soler]
that’s why he’s in jail. . . . [Soler is] not really stressing it because they
think [the petitioner] did it. But [Soler] really did it. . . . You got a little
nosy and asked him how it went down. And [Soler] told you that [the
petitioner] asked him to come with him to buy some weed from Babcock
Street. . . . [Delgado] had told him that he can get him some good shit
. . . [b]ut . . . to come back in the morning . . . . Then [Soler] said that
he was watching where [Delgado] went in the house so when [Delgado]
gave [the petitioner] the weed and was walking [the petitioner] out, [Soler]
said that he went into his coat pocket and pulled out a 45. He said it was
an old black Colt. . . . [Soler] pulled it out, pointed it and started waving
it around . . . . [Soler] sat everybody down . . . in the apartment . . . .
[Soler] told [Delgado] take me to the back room where you got the shit
. . . when [Delgado] got up and then turned around and tried to grab the
gun so that [Soler] just squeezed the trigger. Then they started struggling
and . . . the other dudes in the house ran. And [the petitioner] ran out on
[Soler] . . . . Then [Soler] ran outside, saw [the petitioner] in the front
yard. . . . [E]ven though [the petitioner] didn’t know [Soler] had a gun or
was going to rob [Delgado] that [the petitioner] still shouldn’t have run
out . . . . But for being a bitch now they think [the petitioner] did it so
he’s straight.’’
   2
     The jury found the petitioner not guilty of one count of robbery in the
first degree.
   3
     The respondent urges us not to reach the issue of materiality because
neither the habeas court nor the Appellate Court specifically reached that
issue. Although this is true, reaching the issue is fair to the parties because
the petitioner has asked us to reach the issue in this certified appeal, it is
a question of law arguably within the scope of our certification, and both
parties have briefed the issue—including the petitioner in both his brief and
reply brief. See Kaddah v. Commissioner of Correction, supra, 299 Conn.
136 n.10. Moreover, because the petitioner must prove materiality to succeed
in a Brady challenge, we need not address the underlying question of whether
the state had an undisclosed arrangement with Soler if the lack of disclosure
would otherwise be immaterial.
   4
     The statement was read into the record at trial in relevant part as follows:
‘‘[Soler and I] went back up to the third floor apartment [on Babcock Street].
The dude was in the front porch. We told him we’d take the three dimes
[of marijuana].
   ‘‘The front door was open so he told us to come into the house. I came
in and waited in the living room and [Soler] waited in the hallway. The dude
went into one of the rooms and came out and gave me the weed and I gave
him the money. I was ready to walk out and the dude was right behind me.
[Soler] told me to turn around and go back in. [Soler] was holding a big black
automatic gun. He was pointing it at everyone. . . . [Soler] told everyone
to sit on the couch . . . [and] to run their pockets . . . .
   ‘‘[Soler] told me to take the gun and hold it. I grabbed the gun and [Soler]
started to take everybody’s stuff including money, weed, and jewelry. . . .
I passed [Soler] back the gun . . . . [Soler] told [Delgado] to get up and
show him where the stuff was. [Delgado] got up and he hesitated and then
he turned around and grabbed [Soler]. They started struggling . . . . I heard
the first shot . . . . I ran downstairs . . . . I then heard more shots coming
from inside the building.’’
   5
     The petitioner contended at a suppression hearing during his criminal
trial and during closing argument that this statement was coerced. However,
at the hearing on the motion to suppress the statement, the petitioner
testified that he truthfully told the detectives that he ‘‘went to [the] apart-
ment, [he] committed the crime, it just was [he] didn’t have the gun, it was
[Soler] who was the guy who did the shooting . . . .’’ Although the petitioner
testified at the suppression hearing that he never reviewed the statement
to verify its veracity, and defense counsel, during closing argument, noted
that the petitioner felt that he had to ‘‘give [the police] what they wanted
to hear,’’ the petitioner has never disputed that the statement is correct to
the extent that it placed him at the scene of the crime.
   6
     The state argued at trial that the petitioner was guilty of felony murder
if he, ‘‘either alone or with [Soler], was committing or attempting to commit
robbery or fleeing therefrom and he or [Soler] caused [Delgado’s] death in
the course of doing that or fleeing from that . . . .’’
