
328 A.2d 378 (1974)
George A. BEST, Appellant,
v.
UNITED STATES, Appellee.
No. 7922.
District of Columbia Court of Appeals.
Argued September 24, 1974.
Decided November 20, 1974.
*379 Linda Huber, Washington, D. C., appointed by this court, by appellant.
David T. Stitt, Asst. U. S. Atty., with whom Earl J. Silbert, U. S. Atty., John A. Terry, James F. McMullin, and John C. Lenahan, Asst. U. S. Attys., were on the brief, for appellee.
Before KELLY, FICKLING and NEBEKER, Associate Judges.
NEBEKER, Associate Judge:
This appeal from a jury conviction of robbery in violation of D.C.Code 1973, § 22-2901, presents the issue whether the trial court committed reversible error when it refused to allow appellant to cross-examine a prosecution witness (the arresting officer) in an attempt to show his alleged bias against appellant. We conclude that no reversible error was committed, and affirm.
The robbery occurred on May 7, 1973, in Peoples Drug Store at 2002-14th Street, N.W.[1] The complaining witness, Mrs. Mary Reid, was standing in line at a cash register in order to purchase some money orders. Appellant was in line behind her. Having felt a little nudge on the pocketbook she was carrying, Mrs. Reid noticed that it was open and that her small change purse was missing. She turned around and accused appellant, who was standing behind her, of taking the purse. He denied the charge, left his place in line, and proceeded to walk up an aisle to the front of the store. Mrs. Reid then began to scream for the guard. The floor manager appeared and Mrs. Reid accused appellant of the robbery and pointed him out. At that moment, appellant was standing in another line at the front of the store.
The store manager escorted appellant to an office in the rear of the store. There appellant was patted down but no purse was found. At Mrs. Reid's insistence, the police were then called.
Officers Roberts and Bialasik arrived to investigate the complaint. Officer Roberts, in the presence of Mr. Williams, the store manager, ordered appellant to empty his pockets. Appellant complied, disclosing several bundles (two or three according to Officer Roberts' testimony) *380 of double-folded bills and one $5 bill folded in half. Mrs. Reid at that time was aiding Officer Bialasik in a search for her change purse and, therefore, was not present when the bills were disclosed. The empty purse was found on a shelf in the aisle down which appellant had walked to the other end of the store. Keys and change which were in the purse at the time it was taken were never accounted for.
Although Mr. Best was arrested by Officer Roberts, he was allowed to retain possession of the bills until he was taken to the police station. Officer Roberts testified that at the station he took possession of the bills and for the first time he counted the cash, which amounted to $70 ($65 in double-folded bills[2] and a $5 bill folded in half). The $65 was held as evidence; the $5 bill was returned to Mr. Best.
Both Officer Roberts and Mrs. Reid testified that at no time did Officer Roberts describe to Mrs. Reid the amount, denominations, or condition of the bills seized from appellant. Officer Roberts testified that on May 7, the date of the robbery, Mrs. Reid informed him of the amount of money taken from her and that on May 8 she described the denominations of the bills. According to Officer Roberts, Mrs. Reid described the amount taken only after appellant had been searched and arrested and her purse had been recovered. Upon the officers' arrival, she told them simply that her money and purse had been stolen. The two officers and Mrs. Reid conferred briefly outside the store following the arrest of appellant and the discovery of her purse; they then proceeded to the station house.
Mrs. Reid offered rather lengthy and involved testimony in describing the bills which had been stolen. She recounted that she left home on the morning of the offense with $26, and that she received some additional bills from her sister, Mrs. Rice. She spent a certain amount on various purchases (her sister corroborated portions of the testimony). Mrs. Reid also testified that she had double-folded her bills so that they would fit into her change purse; she also recalled the condition of the various bills, some being older and more worn than others.
On cross-examination of Officer Roberts, defense counsel asked him if he harbored any ill will against Mr. Best. After answering in the negative, Officer Roberts was asked if he was aware that Mr. Best had been hospitalized later in the day of the alleged robbery. Again, his answer was "no". The prosecution initiated a discussion at the bench which resulted in the court's order that that line of cross-examination be terminated. It is this curtailment of questioning that appellant contends constituted reversible error.
From the record, it is apparent that the trial court questioned the relevancy of this line of questioning, and invited a proffer from appellant to explain its purpose. The proffer was as follows:
Your honor, on the day of the incident this officer struck Mr. Best and put him in the hospital and he was taken to the hospital that evening. There is evidence of police brutality and it is admissible to show bias on the part of the police officer.... It's perfectly admissible to show bias.
Appellant's brief clarifies for this court the alleged relevancy of the proposed cross-examination. At trial, such clarification was not offered until the closing argument. The government's case depended entirely on circumstantial evidence, which disclosed that appellant, without explanation, possessed bills, the amount, condition, and denominations of which were positively identified by Mrs. Reid as matching those taken from her. On appeal appellant's theory of the case is that Mrs. Reid was able to identify the bills so *381 precisely only because Officer Roberts had informed her of their condition, amount, and denominations after he had found the money in appellant's possession. (As previously mentioned, both Mrs. Reid and Officer Roberts testified that no such communication ever took place.) Appellant contends that impeachment of Officer Roberts' testimony on this point would necessarily have impaired that of Mrs. Reid. Since the government's case was essentially based on the testimony of these two witnesses regarding identification of the bills, appellant urges that prohibition of his proposed line of cross-examination was fatally prejudicial. Case law discussing the right of cross-examination reveals the following:
Although opportunity to cross-examine is a fundamental right demanding great respect (e. g., Alford v. United States, 282 U.S. 687, 691-692 [51 S.Ct. 218, 75 L.Ed. 624] ... (1931)), the courts have also recognized that regulation of the extent and scope of cross-examination must generally lie within the discretion of the trial court and reversal is warranted only where an abuse of discretion leads to prejudice.... [Howard v. United States, 128 U.S.App. D.C. 336, 341, 389 F.2d 287, 292 (1967) (footnotes omitted).]
The court's ability to prohibit entirely a proposed line of cross-examination is more circumscribed, however. See Alford v. United States, supra, 282 U.S. at 694, 51 S.Ct. 218.
Among the valid objectives of cross-examination is the impeachment of a witness by demonstrating his bias, White v. United States, D.C.App., 297 A.2d 766, 768 (1972). It has been stated that bias of a witness is "always relevant." Villaroman v. United States, 87 U.S.App.D.C. 240, 241, 184 F.2d 261, 262 (1950).
A party's right to undertake demonstration of the bias of his adversary's witness coexists on the same plane with the adversary's prerogative to use the witness. Such an effort may properly solicit over a wide range any information of potential value to the trier of fact in the assessment of credibility.... [Wynn v. United States, 130 U.S.App. D.C. 60, 62, 397 F.2d 621, 623 (1967) (footnotes omitted).]
The record clearly reveals that the trial court misconceived the test for evaluating whether appellant's proposed questioning was probative on the issue of Officer Roberts' alleged bias. Following appellant's proffer, the prosecution stated, "[T]here is no evidence that this officer has struck this man before the incident. And what he did after the incident has nothing to do with the evidence in this case."
As a matter of law, the time of testimony rather than the time of the commission of the alleged offense was the crucial one regarding the tendency of the alleged striking to show bias. See Wynn v. United States, supra at 63 n. 12, 397 F.2d at 624 n. 12, citing cases. That is, the alleged striking needed only to have preceded the officer's testimony; it was immaterial that the robbery incident preceded the alleged striking as far as a proffer of testimonial bias was concerned. See Wynn v. United States, supra at 63, 397 F.2d at 624.
Despite the error of the government's assertion, the court appears to have been swayed by it. In forbidding the cross-examination, the court stated:
Well I am not going to allow it because [by the time the alleged beating occurred] the arrest had already been made and the search, and this [alleged beating] was all after the money had already [been] taken out of his [appellant's] pockets.
It is nonetheless necessary to consider whether the court was justified on other grounds for prohibiting the questioning. Appellant's proffer failed to propose *382 in what way the alleged bias of Officer Roberts was ultimately related to the question of guilt or innocence. Counsel for Mr. Best also stated that he did not know what had prompted the alleged striking at the police station. In this sense, the proffer was incomplete. These deficiencies, however, did not justify the complete curtailment of questioning. An exhaustive proffer is not normally a strict requirement for initiation of a line of cross-examination.[3] And, at any rate, presentation of appellant's proffer was hobbled by the court's misconception of the relevancy matter discussed above.
We conclude that the court's action erroneously curtailed a legitimate defensive endeavor. However, as the court stated in Wynn v. United States, supra, 130 U.S.App.D.C. at 63, 397 F.2d at 624:
[T]his holding does not completely dispose of the matter, for unless the ruling operated detrimentally to appellant we would be obliged to disregard it.... [Footnote omitted.]
See also Hampton v. United States, D.C. App., 318 A.2d 598, 600 (1974); United States v. Pugh, 141 U.S.App.D.C. 68, 436 F.2d 222 (1970).[4]
The prohibited line of inquiry could have been ultimately valuable for appellant's defense only if it had tended to lead the jury through the following series of conclusions: (1) as a matter of fact, Officer Roberts struck appellant at the station house; (2) the striking was of a sort which tended to establish ill will on the part of Officer Roberts toward appellant, as opposed to a justifiable or excusable striking which might not have evidenced any ill will; (3) the alleged ill will reflected at the station house carried over to the time of trial and prompted Officer Roberts specifically to perjure himself in that portion of his testimony where he stated that he had not disclosed the amount or condition of the money to Mrs. Reid prior to her description of it; and (4) Officer Roberts' perjury sufficiently overwhelmed the lengthy testimony of Mrs. Reid so as to give rise to a reasonable doubt as to Mrs. Reid's veracity and, thus appellant's guilt. Failure of the appellant to have convincingly forged any one of the above links in this rather attenuated chain of inferences[5] would have vitiated any *383 potentially significant effect of the proposed testimony.
While, as previously discussed, we find that it was error for the trial court to have completely prohibited the proposed cross-examination, we conclude after reviewing the entire record that such error was harmless. Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). Mrs. Reid's testimony respecting the amount and condition of the bills was critical to the conviction. In the overall context the implied relationship between the alleged bias of Officer Roberts' and Mrs. Reid's testimony depended on such a degree of speculation that no error warranting reversal resulted from prohibiting the proposed line of cross-examination. As did the court in United States v. Pugh, supra, we conclude that appellant "received a fair trial even if not a perfect trial," and therefore his conviction is
Affirmed.
NOTES
[1]  Since appellant presented no evidence at trial, the facts as here stated reflect the presentation of government witnesses.
[2]  The $65 consisted of one $20 bill, four $10 bills, and five $1 bills.
[3]  Counsel often cannot know in advance what pertinent facts may be elicited on cross-examination. For that reason it is necessarily exploratory; and the rule that the examiner must indicate the purpose of his inquiry does not in general apply. ... It is the essence of a fair trial that reasonable latitude be given the cross-examiner, even though he is unable to state to the court what facts a reasonable cross-examination might develop.... To say that prejudice can be established only by showing that the cross-examination, if pursued, would necessarily have brought out facts tending to discredit the testimony in chief, is to deny a substantial right and withdraw one of the safeguards essential to a fair trial.... [Alford v. United States, supra, 282 U.S. at 692, 51 S.Ct. at 219; citations omitted.]

Our finding of error in the instant case is guided by the above language. We do not, however, read this language to preclude our finding that such error was harmless on the particular facts before us. In Alford, defense counsel was prohibited from asking a government witness where he was residing. Counsel apparently suspected that the witness was in federal custody. The Supreme Court was loath to speculate regarding the effect of this prohibition. We conclude, however, that the facts before us establish lack of prejudice beyond a reasonable doubt, and thus we so hold. Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967).
[4]  Recently, in Davis v. Alaska, 415 U.S. 308, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974), the Supreme Court used strong language suggesting that any prevention of cross-examination intended to establish bias constitutes reversible error. We distinguish that case from the one at bar on its facts, however. In Davis the Court found reversible error when cross-examination was curtailed where the witness being questioned was the only eyewitness to the crime and the basis for his claimed bias was fully demonstrated.
[5]  It must be kept in mind that appellant had presented no witness to establish any of the above, and the decision had apparently been made that appellant would not testify in his own defense.
