Compiled Laws, Chapter 168. Michigan Election Law § 168.370a

Sec. 370a. Notwithstanding the provisions of section 370,  1 if a vacancy occurs in an elective or appointive township office, which vacancy is filled by appointment by the township board or the board of county election commissioners and the vacancy occurs more than 7 days before the nominating petition filing deadline as provided in section 349  2 for the general November election that is not the general November election at which a successor in office would be elected if no vacancy, then 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.