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There are no federal statutes or Rules of the Senate that directly affect the status of a Senator who has been indicted for a crime that constitutes a felony. No rights or privileges are forfeited under the Constitution, statutory law, nor the Rules of the Senate upon an indictment. Under the Rules of the Senate, therefore, an indicted Senator may continue to participate in congressional proceedings and considerations.
Under the United States Constitution, a person under indictment is not disqualified from being a Member of or a candidate for reelection to Congress. Internal party rules in the Senate may, however, provide for certain steps to be taken by an indicted Senator. For example, the Senate Republican Conference Rules require an indicted chairman or ranking Member of a Senate committee, or a member of the party leadership, to temporarily step aside from his or her leadership or chairmanship position.
Members of Congress do not automatically forfeit their offices upon conviction of a crime that constitutes a felony.
No express constitutional disability or “disqualification” from Congress exists for the conviction of a crime, other than under the Fourteenth Amendment for certain treasonous conduct by someone who has taken an oath of office to support the Constitution.
Unlike Members of the House, Senators are not instructed by internal Senate Rules to refrain from voting in committee or on the Senate floor once they have been convicted of a crime which carries a particular punishment. Internal party rules in the Senate may affect a Senator’s position in committees. Under the Senate Republican Conference Rules, for example, Senators lose their chairmanships of committees or ranking Member status upon conviction of a felony.
https://fas.org/sgp/crs/misc/RL34716.pdf