Vt. Const. art. II, § 54

[Incompatible offices] No person in this State shall be capable of holding or exercising more than one of the following offices at the same time: Governor, Lieutenant-Governor, Justice of the Supreme Court, Treasurer of the State, member of the Senate, member of the House of Representatives, Surveyor-General, or Sheriff. Nor shall any person holding any office of profit or trust under the authority of Congress, other than a member of the commissioned or enlisted personnel in the reserve components of the armed forces of the United States while not on extended active duty, be eligible to any appointment in the Legislature, or to any executive or judiciary office under this State.