Mich. Comp. Laws § 168.269
If a vacancy occurs in the office of county road commissioner, a qualified person shall be appointed to fill the vacancy by the county board of commissioners. The person appointed shall take the oath of office, give bond in the manner required by law, and hold office for the remainder of the unexpired term and until a successor is elected and qualified. However, in a county in which county road commissioners are elected, if the vacancy occurs more than 7 days before the nominating petition filing deadline as provided in section 254 for the general November election that is not the general November election at which a successor in office would be elected if there were no vacancy, the person appointed shall hold office only until a successor is elected at the next general November election in the manner provided by law and qualifies for office. The successor shall hold the office for the remainder of the unexpired term.
MCL 168.269