Mich. Comp. Laws § 168.84

Sec. 84. Whenever a vacancy shall occur in the office of secretary of state or attorney general, the governor shall appoint a successor to fill such vacancy and the person so appointed shall take the oath of office, give bond in the manner required by law and shall hold such office until his successor is elected and qualified. The candidate receiving the highest number of votes for either of said offices who has subscribed to the constitutional oath and filed the requisite bond shall be deemed to be elected and qualified even though a vacancy occurs prior to the time he shall have entered upon the duties of his office.