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 LUIS DIAZ v. COMMISSIONER OF CORRECTION
                 (AC 34760)
            DiPentima, C. J., and Alvord and Mintz, Js.
       Argued April 8—officially released September 9, 2014

  (Appeal from Superior Court, judicial district of
               Tolland, Newson, J.)
  Michael Zariphes, assigned counsel, for the appel-
lant (petitioner).
   Adam E. Mattei, deputy assistant state’s attorney,
with whom, on the brief, were John C. Smriga, state’s
attorney, Howard S. Stein, senior assistant state’s attor-
ney, and Craig P. Nowak, senior assistant state’s attor-
ney, for the appellee (respondent).
                          Opinion

   ALVORD, J. The petitioner, Luis Diaz, appeals follow-
ing the denial of his petition for certification to appeal
from the judgment of the habeas court denying his
amended petition for a writ of habeas corpus. On
appeal, the petitioner claims that the habeas court
abused its discretion in denying his petition for certifica-
tion to appeal because the court improperly (1) rejected
his claim of ineffective assistance of trial counsel, and
(2) concluded that he failed to prove that the state
suppressed exculpatory evidence at his criminal trial
in violation of Brady v. Maryland, 373 U.S. 83, 87, 83
S. Ct. 1194, 10 L. Ed. 2d 215 (1963). The petitioner also
claims that the habeas court abused its discretion in
denying his motion for rectification and request for an
evidentiary hearing pursuant to State v. Floyd, 253
Conn. 700, 756 A.2d 799 (2000). We dismiss the petition-
er’s appeal.
   The facts giving rise to this case are set forth in State
v. Diaz, 302 Conn. 93, 25 A.3d 594 (2011). ‘‘On the
evening of January 11, 2006, the victim, Philip Tate, was
shot and killed outside a bar known as the Side Effect
West in the city of Bridgeport. Thereafter, the [peti-
tioner] was arrested and charged with murdering the
victim [in violation of General Statutes § 53a-54a], car-
rying a pistol without a permit [in violation of General
Statutes § 29-35,] and criminal possession of a pistol or
revolver [in violation of General Statutes § 53a-217c].
In March, 2006, Corey McIntosh gave a statement to
the police indicating that the [petitioner] had been the
shooter. At that time, McIntosh was on federal proba-
tion and had received a three year suspended sentence
for possessing narcotics in Connecticut. McIntosh testi-
fied at the [petitioner’s] trial that he had seen the [peti-
tioner] outside the Side Effect West immediately before
the shooting and had heard shots as he entered the bar.
He then ran out the back door and saw the [petitioner]
running down the street with a gun in his hand. Addi-
tional state narcotics charges were pending against
McIntosh at the time of trial. He testified that, while
no promises had been made in connection with the
pending charges, he was hoping to receive some consid-
eration in exchange for his testimony.
   ‘‘At some point after July, 2006, Eddie Ortiz wrote a
letter to the prosecutor’s office indicating that he had
information about the murder. He was incarcerated at
the time and stated in his letter that he was looking for
some consideration in exchange for his testimony. Ortiz
testified at the [petitioner’s] trial that he had seen the
[petitioner] shoot the victim. He also testified that, dur-
ing the trial, he had been placed in the same holding
cell as the [petitioner], who said to him, ‘You know
what I did’ and ‘I know where you live at.’ In addition,
Ortiz testified that the [petitioner] had offered him
$5000 not to testify. He further testified that the prosecu-
tor’s office had not promised him anything in exchange
for his testimony and that he had been told that it would
be up to a judge whether he would receive any benefit,
such as a sentence modification. He had expectations,
however, that his testimony would be taken into consid-
eration.1
   ‘‘Approximately six months after the murder, James
Jefferson asked his attorney to inform Harold Dimbo,
a detective with the Bridgeport police department, that
Jefferson had information about the murder. Jefferson,
who was incarcerated in Connecticut on domestic vio-
lence charges at the time, was subject to lifetime parole
in New York in connection with a conviction on narcot-
ics charges in that state. Dimbo visited Jefferson in
prison and Jefferson agreed to give a statement about
the shooting. Dimbo made no promises to Jefferson. In
September, 2006, the domestic violence charges were
dismissed for lack of evidence. Thereafter, Jefferson
testified at the [petitioner’s] trial that he had seen the
[petitioner] and the victim outside Side Effect West
immediately before the shooting. He also saw the [peti-
tioner] shoot at someone, but he did not see the victim
at that point. At the time of trial, Jefferson was incarcer-
ated in Connecticut for violating his parole in New York.
  ‘‘McIntosh, Ortiz and Jefferson were the only wit-
nesses who identified or implicated the [petitioner] as
the shooter. The [petitioner’s] girlfriend, Shenisha
McPhearson, testified that the [petitioner] had been
with her at her apartment at the time of the shooting.
The state presented no physical evidence to tie the
[petitioner] to the shooting and the gun used in the
shooting was never recovered.’’ (Footnotes omitted.)
Id., 95–97.
  Following the trial, the jury returned a verdict of
guilty on all three counts, and on June 8, 2007, the court
sentenced the petitioner to seventy years incarceration.
The petitioner appealed directly to our Supreme Court
pursuant to General Statutes § 51-199 (b) (3), and the
court upheld the conviction. Id., 93.
   In April, 2012, the petitioner filed a third amended
petition for a writ of habeas corpus, which included
claims of ineffective assistance of trial counsel and
substantive constitutional violations of the petitioner’s
due process rights under the state and federal constitu-
tions and Brady v. Maryland, supra, 373 U.S. 83.2 Fol-
lowing a three day evidentiary hearing, the habeas court
denied the habeas petition on May 16, 2012, and subse-
quently denied the petitioner’s petition for certification
to appeal on May 30, 2012. The petitioner appealed to
this court.
  We begin by setting forth the standard of review
and legal principles that guide our resolution of the
petitioner’s appeal. ‘‘Faced with the habeas court’s
denial of certification to appeal, a petitioner’s first bur-
den is to demonstrate that the habeas court’s ruling
constituted an abuse of discretion. Abuse of discretion
is the proper standard because that is the standard to
which we have held other litigants whose rights to
appeal the legislature has conditioned upon the
obtaining of the trial court’s permission. . . . If the
petitioner succeeds in surmounting that hurdle, the peti-
tioner must then demonstrate that the judgment of the
habeas court should be reversed on its merits. . . .
To prove an abuse of discretion, the petitioner must
demonstrate that the [resolution of the underlying claim
involves issues that] are debatable among jurists of
reason; that a court could resolve the issues [in a differ-
ent manner]; or that the questions are adequate to
deserve encouragement to proceed further. . . . If this
burden is not satisfied, then the claim that the judgment
of the habeas court should be reversed does not qualify
for consideration by this court.’’ (Internal quotation
marks omitted.) Patterson v. Commissioner of Correc-
tion, 150 Conn. App. 30, 34, 89 A.3d 1018 (2014). Having
set forth the appropriate standard of review, we next
consider each of the petitioner’s claims.
                             I
  The petitioner first claims that the habeas court
improperly rejected his claim of ineffective assistance
of his trial counsel. He argues that trial counsel ren-
dered ineffective assistance by failing to investigate and
present the testimony of Clifton Waiters, Jacqueline
Cooper, and Eugene Browne, who would have ‘‘injected
a great deal of reasonable doubt as to the petitioner
being the perpetrator of the charged crimes.’’3 We are
not persuaded.
   ‘‘In Strickland v. Washington, 466 U.S. 668, 104 S.
Ct. 2052, 80 L. Ed. 2d 674 (1984), the United States
Supreme Court enunciated the two requirements that
must be met before a petitioner is entitled to reversal
of a conviction due to ineffective assistance of counsel.
First, the [petitioner] must show that counsel’s perfor-
mance was deficient. . . . Second, the [petitioner]
must show that the deficient performance prejudiced
the defense. . . . Unless a [petitioner] makes both
showings, it cannot be said that the conviction . . .
resulted from a breakdown in the adversarial process
that renders the result unreliable. . . . A reviewing
court need not address both components of the inquiry
if the [petitioner] makes an insufficient showing on
one.’’ (Citation omitted; internal quotation marks omit-
ted.) Ramey v. Commissioner of Correction, 150 Conn.
App. 205, 209–210, 90 A.3d 344, (2014).
   In his petition for a writ of habeas corpus, the peti-
tioner identified Waiters, Cooper, and Browne as ‘‘third
party culpability witness[es].’’ It is well established that
‘‘a defendant may introduce evidence which indicates
that a third party, and not the defendant, committed
the crime with which the defendant is charged. . . .
The defendant, however, must show some evidence
which directly connects a third party to the crime with
which the defendant is charged. . . . It is not enough
to show that another had the motive to commit the
crime . . . nor is it enough to raise a bare suspicion
that some other person may have committed the crime
of which the defendant is accused.’’ (Emphasis omitted;
internal quotation marks omitted.) State v. Galarza, 97
Conn. App. 444, 464, 906 A.2d 685, cert. denied, 280
Conn. 936, 909 A.2d 962 (2006).
   In rejecting the petitioner’s ineffective assistance of
counsel and third party culpability claim, the habeas
court found that ‘‘the evidence presented here clearly
indicates that there was no . . . direct connection to
any third party.’’ The court considered the testimony
of each of the three witnesses4 before concluding that
trial counsel was not deficient by failing to present that
evidence, and that it was not prejudicial to the petitioner
for that evidence not to have been presented at trial.
Now before us, the petitioner broadly argues that the
witnesses’ respective testimonies ‘‘would all have been
helpful in establishing the asserted defense of misidenti-
fication [and] may have even helped in establishing a
third party culpability defense.’’ Despite this assertion,
he points to no testimony that directly connects a third
party to the crime. ‘‘The failure of defense counsel to
call a potential defense witness does not constitute
ineffective assistance unless there is some showing that
the testimony would have been helpful in establishing
the asserted defense. . . . In the absence of that show-
ing by [a] petitioner, we are unable to conclude that
[the petitioner] was prejudiced by counsel’s failure to
interview the [witness].’’ (Internal quotation marks
omitted.) Smith v. Commissioner of Correction, 141
Conn. App. 626, 635, 62 A.3d 554, cert. denied, 308 Conn.
947, 67 A.3d 290 (2013). Accordingly, the petitioner has
not established that he was prejudiced by the actions
of his trial counsel, and he cannot prevail on his claim
of ineffective assistance of counsel. We therefore con-
clude that the habeas court did not abuse its discretion
in denying the petitioner’s petition for certification to
appeal from its denial of this claim.
                            II
   The petitioner also claims that the habeas court
improperly concluded that he failed to prove that the
state suppressed exculpatory evidence at his criminal
trial in violation of Brady v. Maryland, supra, 373 U.S.
87. Specifically, the petitioner maintains that ‘‘the dis-
crepancy between the prosecutor’s representations to
the jury during his closing argument [at the petitioner’s
criminal trial] in [April, 2007] that Ortiz was promised
flat out no benefit and the prosecutor’s later consent to
Ortiz’ sentence modification application [in September,
2007] represents an undisclosed implied and/or infor-
mal understanding/agreement between Ortiz and the
state that if he testified favorably, the state would con-
sent to his sentence modification application and then
support him at the hearing on such application.’’ We
are not persuaded.
   ‘‘The law governing the state’s obligation to disclose
exculpatory evidence to defendants in criminal cases
is well established. The defendant has a right to the
disclosure of exculpatory evidence under the due pro-
cess clauses of both the United States constitution and
the Connecticut constitution. Brady v. Maryland,
[supra, 373 U.S. 86]; State v. Simms, 201 Conn. 395, 405
[and] n.8, 518 A.2d 35 (1986). In order to prove a Brady
violation, the defendant must show: (1) that the prose-
cution suppressed evidence after a request by the
defense; (2) that the evidence was favorable to the
defense; and (3) that the evidence was material.’’ (Inter-
nal quotation marks omitted.) State v. Guilbert, 306
Conn. 218, 271, 49 A.3d 705 (2012). ‘‘It is well established
that [i]mpeachment evidence as well as exculpatory
evidence falls within Brady’s definition of evidence
favorable to an accused. . . . A plea agreement
between the state and a key witness is impeachment
evidence falling within the definition of exculpatory
evidence contained in Brady.’’ (Citations omitted; inter-
nal quotation marks omitted.) State v. Floyd, supra, 253
Conn. 736–37.
   ‘‘The question of whether there existed an agreement
between [a witness] and the state is a question of fact.
. . . When reviewing the decision of a habeas court,
the facts found by the habeas court may not be dis-
turbed unless the findings were clearly erroneous. . . .
This court does not retry the case or evaluate the credi-
bility of the witnesses. . . . Rather, we must defer to
the [trier of fact’s] assessment of the credibility of the
witnesses based on its firsthand observation of their
conduct, demeanor and attitude. . . . The habeas
judge, as the trier of facts, is the sole arbiter of the
credibility of witnesses and the weight to be given to
their testimony.’’ (Internal quotation marks omitted.)
Lewis v. Commissioner of Correction, 116 Conn. App.
400, 407, 975 A.2d 740, cert. denied, 294 Conn. 908, 982
A.2d 1082 (2009).
  In support of his position, the petitioner directs us
to (1) the prosecutor’s closing argument wherein he
advised the jurors that Ortiz was ‘‘promised nothing’’
and ‘‘flat out told [that he would] get no benefit’’ for his
testimony; (2) Ortiz’ sentence modification application
revealing the prosecutor’s signature concurring with
the application; (3) Ortiz’ subsequent modification of
his sentence several months after the petitioner was
sentenced; and (4) Ortiz’ August, 2007 letter to the pros-
ecutor thanking him for ‘‘fulfilling his promise.’’ The
habeas court considered all of this evidence, as well as
testimony from the prosecutor and trial counsel, and
found that there was ‘‘no proof that there was an under-
standing either in the courthouse with [the prosecutor]
or afterwards’’ that Ortiz was going to be granted some
kind of benefit for testifying. Instead, the court found
that all that Ortiz was told with respect to a possible
sentence modification was that if he ‘‘[made] a pitch to
the judge for what [he] testified to [after the petitioner’s
trial] and that . . . judge would consider it, then so be
it.’’5 We defer to the court’s credibility determination
and factual findings and conclude, on the basis of our
review of the evidence, that the court’s finding that the
petitioner failed to prove the existence of an agreement
between Ortiz and the state was not clearly erroneous.
See Lewis v. Commissioner of Correction, supra, 116
Conn. App. 408. Accordingly, the habeas court properly
denied certification on this ground of the petitioner’s
claim.
                            III
  Finally, the petitioner argues that the habeas court
abused its discretion in denying the petitioner’s motion
for rectification and request for an evidentiary hearing
pursuant to State v. Floyd, supra, 253 Conn. 700.6 We
are not persuaded.
  The following procedural history is necessary for our
resolution of this claim. While the present appeal was
pending, the petitioner filed a motion for rectification
with this court seeking an evidentiary hearing to add
to the record a transcript of a sentence modification
hearing that had occurred in State v. Ortiz, Superior
Court, judicial district of Fairfield, Docket No. CR-06-
0213538 (August 20, 2007). This court forwarded the
motion to the habeas court pursuant to Practice Book
§ 66-5,7 and the habeas court denied the motion. The
petitioner filed a motion for review with this court,
and we granted the petitioner’s motion for review, but
denied the relief requested therein without prejudice
to ‘‘brief the propriety of the filing of his motion for
rectification and his request for an evidentiary ‘Floyd
type’ hearing in his brief on the merits.’’
   Practice Book § 66-5 defines a motion for rectifica-
tion as ‘‘a motion seeking corrections in the transcript
. . . .’’ (Emphasis added.) ‘‘[W]e review the actions of
the habeas court on the record and may not consider
extraneous material later submitted directly to us
. . . .’’ Young v. Commissioner, 104 Conn. App. 188,
194, 932 A.2d 467 (2007), cert. denied, 285 Conn. 907,
942 A.2d 416 (2008). Here, it is clear that the petitioner
knew about Ortiz’ sentence modification at the time
of the habeas court’s hearing on the petitioner’s third
amended petition for a writ for habeas corpus, and that
he did not enter or attempt to enter a transcript of the
Ortiz resentencing hearing into evidence at that time.
Instead, the petitioner first submitted the transcript to
the court approximately six months after the court
denied the habeas petition and the petition for certifica-
tion to appeal. The petitioner cannot use a motion for
rectification as a method of introducing new evidence
to the habeas court after the hearing that he knew about
during the habeas hearing. See State v. Hamlin, 90
Conn. App. 445, 878 A.2d 374 (declining defendant’s
request to remand for an evidentiary hearing pursuant
to Floyd because record demonstrated that defendant
was aware, prior to the suppression hearing and trial,
of the information he sought to include in the record),
cert. denied, 276 Conn. 914, 888 A.2d 86 (2005). Accord-
ingly, the habeas court properly concluded that it could
not accept or consider the transcript following its ren-
dering judgment, and we affirm the denial of the motion
for rectification.
   For the foregoing reasons we conclude that the peti-
tioner has not demonstrated that the issues he has
raised in the petition for certification to appeal are
debatable among jurists of reason, that a court could
resolve those issues differently or that the questions
raised deserve encouragement to proceed further. Con-
sequently, the petitioner has failed to demonstrate that
the court abused its discretion in denying his petition
for certification to appeal.
      The appeal is dismissed.
      In this opinion the other judges concurred.
  1
     The record reveals that in September, 2007, Ortiz submitted a sentence
modification application. The prosecutor concurred with the sentence modi-
fication request. The court granted the application, and reduced Ortiz’ sen-
tence from eight years imprisonment to three years to serve.
   2
     The petitioner also claimed actual innocence and ineffective assistance
of appellate counsel. The actual innocence claim was withdrawn by the
petitioner, and, because evidence had already commenced, the habeas court
dismissed the claim with prejudice on May 16, 2012. The ineffective assis-
tance of appellate counsel claim also was dismissed by the habeas court
on May 16, 2012. The petitioner has not challenged these rulings on appeal.
   3
     In support of his ineffective assistance of counsel claim, the petitioner
also claims that trial counsel should have presented the testimony of Jill
Bellao at the jury trial. A review of the habeas petition reveals that the
petitioner identified eighteen witnesses that trial counsel failed to call. Bellao
was not included on that list, nor was she specifically identified anywhere
else in the petition. ‘‘It is well settled that [t]he petition for a writ of habeas
corpus is essentially a pleading and, as such, it should conform generally
to a complaint in a civil action. . . . It is fundamental in our law that the
right of a plaintiff to recover is limited to the allegations of his complaint.
. . . While the habeas court has considerable discretion to frame a remedy
that is commensurate with the scope of the established constitutional viola-
tions . . . it does not have the discretion to look beyond the pleadings
and trial evidence to decide claims not raised.’’ (Internal quotation marks
omitted.) Fulton v. Commissioner of Correction, 126 Conn. App. 706, 713–14,
12 A.3d 1058, cert. denied, 300 Conn. 937, 17 A.3d 473 (2011). Although
Bellao testified before the habeas court regarding the petitioner’s employ-
ment around the time of the shooting, the petitioner never presented the
habeas court with the opportunity to address the issue of whether trial
counsel’s failure to call Bellao in the underlying criminal trial was deficient
or prejudicial. ‘‘This court is not bound to consider claimed errors unless
it appears on the record that the question was distinctly raised . . . and
was ruled upon and decided by the court adversely to the appellant’s claim.
. . . To review [the claim] now would amount to an ambuscade of the
[habeas] judge. . . . This court is not compelled to consider issues neither
alleged in the habeas petition nor considered at the habeas proceeding
. . . .’’ (Internal quotation marks omitted.) Id., 714. Accordingly, we do not
consider the petitioner’s claim on appeal with respect to Bellao.
   4
     The court concluded that Waiters’ testimony ‘‘at best indicates that he
believed that the individual he saw run by him may have been dark skinned,’’
and that there had ‘‘been no evidence presented . . . as to how, even if
presented—since there was additional evidence at trial as to the potential
issue with the skin tone or skin color of the shooter—how . . . Waiters’
testimony in addition to that other testimony would have in and of itself
changed the outcome of the hearing.’’ Similarly, the court found that ‘‘even
accepting everything . . . [Cooper] said, all she said was that the victim
claimed, they set me up’’ and that there was ‘‘no real likelihood that it would
have had any effect on the outcome of the trial because all it would seem
to indicate was that the victim expected to meet somebody there, and then
what he expected to happen didn’t happen.’’ Finally, the court noted that
Browne’s testimony was simply that Browne ‘‘wasn’t at the area of the
shooting . . . [that he] didn’t know the victim, and [that he] had nothing
to do with it.’’
   5
     As General Statutes § 53a-39 (b) makes clear, it is ‘‘the sentencing court
or judge,’’ and not the state’s attorney, who ‘‘may, after hearing and for
good cause shown, reduce the sentence’’ of a defendant.
   6
     ‘‘Pursuant to State v. Floyd, supra, 253 Conn. 700, a trial court may
conduct a posttrial evidentiary hearing to explore claims of potential Brady
violations . . . when a defendant was precluded from perfecting the record
due to new information obtained after judgment. . . . In order to warrant
such a hearing, a defendant must produce prima facie evidence, direct or
circumstantial, of a Brady violation unascertainable at trial.’’ (Citations
omitted; internal quotation marks omitted.) State v. Ouellette, 295 Conn.
173, 182 n.7, 989 A.2d 1048 (2010).
   7
     Practice Book § 66-5 provides in relevant part: ‘‘The appellate clerk shall
forward the motion for rectification . . . and the opposition, if any, to the
trial judge who decided, or presided over, the subject matter of the motion
for rectification . . . for a decision on the motion. If any party requests it
and it is deemed necessary by the trial court, the trial court shall hold a
hearing at which arguments may be heard, evidence taken or a stipulation
of counsel received and approved. The trial court may make such corrections
or additions as are necessary for the proper presentation of the issues raised
or for the proper presentation of questions reserved. The trial judge shall
file the decision on the motion with the appellate clerk. . . .’’
