What role does the supreme court have in the impeachment process of the executive branch?

The Supreme Court has never held that executive privilege applies in the impeachment context. Instead, it created the privilege in the context of a dispute about discovery of communications between President Nixon and White House advisors in a criminal case not aimed at Nixon himself, but at his advisors and campaign staff. Nixon was only an unindicated co-conspirator in that case. Because of the case’s context, the Court focused on balancing the President’s confidentiality interests against the judicial system’s need to reach a just verdict in a criminal case.