Cross-examination of complainant was proper for the purpose of impeachment (People v Schwartzman, 24 NY2d 241, 245, cert denied 396 US 846; Richardson, Evidence § 491 [Prince 10th ed]; Fisch, Evidence § 486 [2d ed]). Bias, interest, or hostility of a witness is not collateral (see, People v Webster, 139 NY 73), nor is a matter collateral when it is relevant to impeach a witness by showing a motive to lie (see, People v Brown, 26 NY2d 88, 94; People v Crandall, 48 AD2d 946, 947). Here, the issue of an allegedly false prior accusation was relevant (see, People v Hill, 52 AD2d 609, 611; People v Moore, 23 AD2d 854).
The theory of the defense was that on the night of the alleged crime, the complainant was with men of whom her father did not approve and that the complainant, who admittedly was intoxicated, had lied to her father to avoid punishment as she had done in the past. The truth or falsity of the prior accusation was relevant on the question of the complainant’s motive falsely to accuse defendant, i.e., whether her fear of her father was so great that she would falsely make a serious accusation in order