The United States Supreme Court has held that a defendant witness may be impeached on cross-examination by evidence which is unlawfully obtained and not admissible in the Government's case in chief provided that the questions on cross-examination are reasonably related to matters covered on direct examination.
United States v. Havens, 446 U.S. 620 (1980).
Francis C. Rapp Jr.,
Constitutional Law - Fourth Amendment - Search and Seizure - Impeachment - Cross-Examination,
Duq. L. Rev.
Available at: https://dsc.duq.edu/dlr/vol19/iss4/6