If a criminal defendant offers evidence of his or her character circumstantially - to show he or she did not commit the crime charged -- the prosecution can offer rebutting evidence of defendant's character.

See United States v. Crump, 934 F.2d 947, 954-955 (8th Cir. 1991) (upholding trial court's admission of witness's testimony relating to accused's prior bad acts of distributing drugs because accused asserted the defense of entrapment, and such evidence was admissible to prove his predisposition to...A subjective entrapment defense makes an accused's criminal liability contingent on a finding of the accused's predisposition or the accused's lack of predisposition to commit the crime charged and since criminal predisposition is a character trait, the defense of subjective entrapment makes accused's character an element of either a defense or a criminal charge, evidence of accused's criminal predisposition -- including evidence in the form of reputation, opinion, and evidence of specific instances of accused's conduct -- is not barred by the rule against the use of a person's character to show the person's conduct.

Fed. R. Evid. 611(b) ("Cross-examination should be limited to the subject matter of the direct examination and matters affecting the credibility of the witness.").Apart from a party's right to impeach a witness, the permissible scope of a party's cross-examination of a witness following the testimony of the witness on direct examination for an opposing party is limited to the subject matter of the testimony of the witness on direct examination.

United States v. Hunt, 521 F.3d 636, 643 (6th Cir. 2008) (upholding trial court's refusal to admit the statements from an affidavit under Rule 804(b)(1) because (1) "[defendant] has not demonstrated that the....The hearsay exception for prior testimony applies only if testimony was in fact previously given.