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.

Fed. R. Evid. 408(b) ("This rule does not require exclusion if the evidence is offered for purposes not prohibited by subdivision (a). Examples of permissible purposes include ... proving an effort to obstruct a criminal investigation or prosecution.").Although settlement negotiations and offers are inadmissible (i) to show the validity or invalidity of a claim when validity is in dispute, (ii) to show the amount of damages when the amount is in dispute, or (iii) to impeach by showing a prior inconsistent statement or specific contradiction, settlement evidence is admissible to show an attempt to obstruct a criminal investigation or prosecution.

United States v. Brun, 416 F.3d 703, 707 (8th Cir. 2005) (upholding trial court's admission of Carlson's and Oakgrove's statements which did not violate defendant's rights under the Confrontation Clause because the....The right of confrontation guaranteed by the Confrontation Clause of the Sixth Amendment to the U.S. Constitution puts no constraints on the admissibility of nontestimonial hearsay statements; the federal constitutional right of confrontation does not apply to such statements.

Cf. United States v. Lawrence, 349 F.3d 109, 117 (3d Cir. 2003) (upholding trial court's exclusion into evidence of the victim's hospital bed identification of another suspect as a dying declaration because defendant failed....The hearsay exception for dying declarations applies only if the declarant believed that his or her own death was imminent when he or she made the statement.