
904 A.2d 377 (2006)
Andre McDONALD, Appellant,
v.
UNITED STATES, Appellee.
No. 04-CM-1201.
District of Columbia Court of Appeals.
Argued December 8, 2005.
Decided August 3, 2006.
*379 Walter S. Booth, Bethesda, MD, appointed by the court, for appellant.
Kathleen J. Monaghan, Assistant United States Attorney, with whom Kenneth L. Wainstein, United States Attorney, John R. Fisher, Assistant United States Attorney at the time the brief was filed, and David B. Goodhand and Zulima Espinel, Assistant United States Attorneys, were on the brief, for appellee.
Before GLICKMAN and KRAMER, Associate Judges, and NEBEKER, Senior Judge.
GLICKMAN, Associate Judge:
Appellant Andre McDonald was convicted after a bench trial on one count of simple assault, a violation of D.C.Code § 22-404 (2001). On appeal, McDonald challenges the trial judge's sua sponte refusal to hear his testimony about the injuries he allegedly suffered during his arrest. McDonald contends that with this decision, the judge abused her discretion and infringed his constitutional right to present a complete defense. We agree, and since we cannot say that the error was harmless, we reverse McDonald's conviction and remand for a new trial.

I.
McDonald was arrested for assaulting his wife, Brenda Harris, when he met her at a restaurant to pick her up after work. On the sidewalk in front of the restaurant, the couple began to argue. McDonald was apparently upset because Harris had been at the restaurant with a male co-worker.
What happened next was disputed at trial. The government's only witness, Metropolitan Police Department ("MPD") Officer David Carter, testified that he happened to be parked across the street from the restaurant, monitoring the area for underage drinking, when he saw McDonald grab Harris by the throat and throw her to the ground. Almost immediately after Carter witnessed this assault, he saw another police officer, Gregory Kurtz, ride up to the couple on a bicycle, dismount, and "put" McDonald on the ground. Carter then left his vehicle and helped Kurtz handcuff and arrest McDonald. (Kurtz did not appear at trial.)
In contrast, McDonald and Harris both testified that McDonald never touched Harris. Rather, they claimed, they were merely having an admittedly heated but purely verbal and non-violent argument when, without warning, Officer Kurtz suddenly "rode up on his bike, dropped [it]. . . and pushed [McDonald] up against the wall." McDonald testified that Officer Kurtz "came up on my left side with his bicycle and I felt the wheel hit my left leg." "The next thing I know," McDonald said, "I'm being bum-rushed," pushed "against the wall" of a building, and then "thrown to the ground and kneeled [sic] with his knee in my back." McDonald and Harris protested in vain that he had done nothing to merit such treatment.
The theory of McDonald's defense was that the assault charge was a fabrication to protect Kurtz and cover up the fact that he had overreacted, rashly intervened without justification, used excessive force, and physically injured McDonald. To support this theory, defense counsel questioned Harris about her husband's injuries, and she reported seeing a bruise on McDonald's arm, some smudges on his shirt, *380 and a scrape on his pants. When counsel cross-examined Officer Carter, however, the officer did not recall noticing that McDonald was hurt in any way.
Defense counsel also sought to question McDonald about his injuries, but he was prevented from doing so. As McDonald began to explain how he was hurt, the trial judge cut him off sua sponte, declaring that she could not see how the testimony was relevant, as the case was not about police brutality but about whether McDonald had assaulted his wife. Defense counsel proffered that the testimony would establish that McDonald was injured during his arrest and that this injury "was visible to the officers on the scene." This fact, counsel contended, "would present the police with a reason to make sure they had some sort of charge to cover themselves in case of a complaint or something to that effect." The judge was not persuaded by this argument, and after the bench conference, defense counsel had no further questions to ask his client.
When the trial judge delivered her verdict at the conclusion of this one-day bench trial, she made no express finding as to whether McDonald had or had not been injured during his arrest. Stating, however, that the police had no motive to arrest McDonald without cause, the judge disbelieved McDonald and Harris and credited Officer Carter's testimony that McDonald assaulted his wife. Accordingly, the judge found McDonald guilty of simple assault and imposed a sixty-day suspended sentence with one year of supervised probation. From this judgment McDonald appeals, focusing his challenge primarily on the preclusion of his testimony regarding his injuries.

II.
"Whether rooted directly in the Due Process Clause ..., or in the Compulsory Process or Confrontation clauses of the Sixth Amendment, the Constitution guarantees criminal defendants a meaningful opportunity to present a complete defense." Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986) (citation and internal quotation marks omitted). Among other things, we have said, this guarantee means that defendants must be afforded "some opportunity"a fair and meaningful opportunityto show that the government's witnesses are biased. Hollingsworth v. United States, 531 A.2d 973, 979 (D.C.1987) (citation and internal quotation marks omitted). A defendant may demonstrate such bias not only by cross-examining the witnesses, but also with extrinsic evidence. Id. (citation omitted). If the trial court erroneously impaired the exercise of this constitutional right, and the objection to the error has been preserved, the defendant's conviction may stand only if the error was harmless beyond a reasonable doubt. Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967).
McDonald argues that, in preventing him from testifying about his injuries, the trial judge in this case committed a constitutional violation. He contends that this testimony was central to his theory of bias (namely, that Officer Carter lied about the assault to cover up the fact that his fellow officer apprehended McDonald for no reason and injured him in the process). Although the government responds that McDonald's testimony was repetitive if not irrelevant and that the judge properly exercised her discretion in excluding it, we are persuaded that McDonald is correct. The trial judge erred, the error was of constitutional magnitude, and it was not harmless.
First, the trial court was mistaken in viewing evidence of what she termed police brutality to be irrelevant. Where *381 the prosecution rests on the credibility of the arresting police officers, and the theory of defense is that the charge is a fabrication, evidence of excessive use of force by the police plainly is relevant, as it could demonstrate the witnesses' bias against the defendant. See Blair v. United States, 130 U.S.App. D.C. 322, 324, 401 F.2d 387, 389 (1968) ("It is of course clear that the range of evidence that may be elicited for the purpose of establishing bias of a witness is quite broad and that accordingly evidence of police brutality is admissible for such purposes."); see also Hollingsworth, 531 A.2d at 979. Moreover, contrary to the government's contention, the defense did not "manufacture [its] allegations of bias out of thin air...." See Clayborne v. United States, 751 A.2d 956, 962-63 (D.C.2000). These allegations were based on a "well-reasoned suspicion," which counsel proffered to the trial court: that Officer Carter gave false testimony about seeing McDonald assault his wife because he did not want his fellow officer to get in trouble for injuring a man he arrested without cause. See id. While defense counsel did not proffer specific facts regarding Carter's proclivity to cover up for his fellow officers, he was not required to do so. See, e.g., Carter v. United States, 614 A.2d 913, 919 (D.C.1992) (observing that District of Columbia case law is "fairly lenient" in the foundation it requires before defense counsel may launch into a line of questioning aimed at illustrating a witness' bias); Best v. United States, 328 A.2d 378, 382 (D.C.1974) (noting that "an exhaustive proffer is not normally a strict requirement for" allowing defense counsel to introduce evidence of police brutality to show bias on the part of a government witness).
Furthermore, McDonald's testimony would not have been, as the government argues, needlessly repetitive. Although defense counsel had questioned two other witnessesCarter and Harrisabout McDonald's injuries, they disagreed over whether McDonald had been visibly hurt during the course of his arrest, and the prosecution certainly did not concede that he was injured. Thus, far from being unduly cumulative, McDonald's testimony as to his own injuries would have been pertinent to a factual dispute on a highly relevant matter. And there were no countervailing considerationsno legitimate concerns, for example, about the danger of unfair prejudice to the prosecution, confusion of the issues, or waste of time and prolongation of the trial, see Johnson v. United States, 683 A.2d 1087, 1099 (D.C.1996) (en banc)that might have supported excluding the testimony.
Because McDonald's testimony about his injuries would have been neither unduly repetitive nor irrelevant, we are constrained to conclude that the trial judge abused her discretion in precluding it. Moreover, the error resulted in an unconstitutional deprivation of McDonald's right to present a complete defense. It may be true that he was able to present some evidence of his injuries through his wife's testimony, and that the Constitution "guarantees a defendant only `an opportunity [to present a defense] ..., not [an opportunity] ... that is effective in whatever way, and to whatever extent, the defense might wish.'" Clark v. United States, 639 A.2d 76, 82 (D.C.1993) (quoting Delaware v. Van Arsdall, 475 U.S. 673, 679, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986)). But for that opportunity to be meaningful, it must be full and fair, not arbitrarily and significantly curtailed. Where a criminal defendant is trying to prove that he was injured during his arrest to support his theory that the police fabricated the charge against him, the defendant cannot be denied the chance to testify about what he himself suffered. As the Second Circuit *382 recently reminded us, trial courts must take particular care to ensure that criminal defendants are allowed to give complete statements when testifying in their own defense. See United States v. Quattrone, 441 F.3d 153, 183 (2d Cir.2006) (noting that the constitutional right to a fair trial "necessarily includes the right to testify on their own behalf" and that concerns about judicial efficiency and fairness must always be balanced against this right) (citation omitted). And where, as here, the evidence without the defendant's excluded testimony has left a factual question central to his bias theory in dispute, we cannot say that the defendant has been afforded a meaningful opportunity to present his defense. See, e.g., Howard v. United States, 656 A.2d 1106, 1118 (D.C.1995) (holding that the defendant's "one cryptic reference" to the fact that the government witness had once shot at him was an insufficient opportunity to prove this fact and thus present the defendant's theory that the witness was biased).[1]
Given both the centrality of McDonald's injuries to his bias defense and the less than overwhelming strength of the prosecution's one-witness case, the erroneous exclusion of McDonald's testimony was not harmless under a Chapman standard of review. The judge made no finding of fact as to whether McDonald was injured, and we cannot say that she would have disbelieved him on that point. Had the judge heard and believed McDonald, we cannot say that she still would have rejected his bias defense. We therefore cannot say "beyond a reasonable doubt" that, had the judge allowed McDonald to testify about his injuries, she still would have believed Officer Carter, the sole witness presented by the government to the alleged assault. Consequently, we must reverse McDonald's conviction and remand for a new trial.[2]
So ordered.
NOTES
[1]  For other cases in which this Court has found that some opportunity to present evidence of bias was still insufficient to satisfy the defendant's Sixth Amendment rights, see, e.g., Jones v. United States, 853 A.2d 146, 153-54 (D.C.2004) (finding a constitutional violation where trial court refused to allow questioning of the police witness about his allegedly defective investigatory procedures, even though the jury had already heard about some of the purported mistakes); Hollingsworth, 531 A.2d at 979-80 (concluding that even though a defense witness had testified that she heard the complaining witness threaten to "get" and to "fix" the defendant, the trial court should have allowed defense counsel to recall this witness to testify that the complaining witness had threatened her that she would be "taken care of too"). Cf. McClellan v. United States, 706 A.2d 542, 548 (D.C.1997) (holding that defendant had ample opportunity to present his bias theory, even without cross-examining the allegedly biased witness, because the main evidence of bias was conceded in the government's opening and closing arguments, by another witness at trial and in a piece of extrinsic evidence).
[2]  McDonald raises a second issue on appeal that we find it unnecessary to reach, namely, whether the trial judge erred in excluding a report written by Officer Kurtz when McDonald sought to introduce it to impeach Officer Carter at the conclusion of the defense case. The issue is not likely to arise in the same way if there is a second trial, if only because McDonald then should have an opportunity to establish that the report was adopted or approved by Carter.
