Compiled Laws, Chapter 168. Michigan Election Law § 168.370

Sec. 370.  (1) Except as provided in section 370a   1 or subsection (2), if a vacancy occurs in an elective or appointive township office, the vacancy shall be filled by appointment by the township board, and the person appointed shall hold the office for the remainder of the unexpired term.

(2) If 1 or more vacancies occur in an elective township office that cause the number of members serving on the township board to be less than the minimum number of board members that is required to constitute a quorum for the transaction of business by the board, the board of county election commissioners shall make temporary appointment of the number of members required to constitute a quorum for the transaction of business by the township board.  An official appointed under this subsection shall hold the office only until the official's successor is elected or appointed and qualified.  An official who is temporarily appointed under this subsection shall not vote on the appointment of himself or herself to an elective or appointive township office.

(3) If a township official submits a written resignation from an elective township office, for circumstances other than a resignation related to a recall election, that specifies a date and time when the resignation is effective, the township board, within 30 days before that effective date and time, may appoint a person to fill the vacancy at the effective date and time of the resignation.  The resigning official shall not vote on the appointment.

(4) Except as provided in subsection (5), if the township board does not make an appointment under subsection (3), or if a vacancy occurs in an elective township office and the vacancy is not filled by the township board or the board of county election commissioners within 45 days after the beginning of the vacancy, the county clerk of the county in which the township is located shall call a special election within 5 calendar days to fill the vacancy.  Not later than 4 p.m. on the fifteenth calendar day after the county clerk calls a special election under this section, the township party committee for each political party in the township shall submit a nominee to fill the vacancy.  The special election shall be held on the next regular election date that is not less than 60 days after the deadline for submitting nominees under this section or 70 days after the deadline for submitting nominees under this section if the next regular election date is the even year August primary or the general November election.  Notice of the special election shall be given in the same manner required by section 653a.  2  A special election called under this section does not affect the rights of a qualified elector to register for any other election.  A person elected to fill a vacancy shall serve for the remainder of the unexpired term.

(5) Subsection (4) does not apply to the office of township constable.  If a vacancy occurs in the office of township constable, the township board shall determine if and when the vacancy shall be filled by appointment.  If the township board does not fill the vacancy by appointment, the office of township constable shall remain vacant until the next general or special election in which township offices are filled.