Mich. Comp. Laws § 47.5
The board of commissioners of any county may appoint a board of county auditors of not to exceed 3 members, 1 of whom the county board of commissioners shall designate as chairperson of the board of county auditors. If the board of county auditors consists of 1 individual, that individual must be appointed for a term of 1 year. If the board consists of 2 individuals, 1 must be appointed for a term of 1 year and 1 must be appointed for a term of 2 years. If the board consists of 3 individuals, 1 must be appointed for a term of 1 year, 1 must be appointed for a term of 2 years, and 1 must be appointed for a term of 3 years. The term of office of each of these members begins on the following January 1. At each October session of the county board of commissioners before the expiration of the term of office of each of the individual members of the board, a successor must be appointed by the county board of commissioners for a term of 3 years from the following January 1. Every person appointed shall hold for the term of office indicated and until his or her successor is appointed and qualified. A person shall not be considered appointed as a member of the board of county auditors who does not receive a majority vote of all the members of the county board of commissioners. If a vacancy occurs in the board of county auditors, the vacancy must be filled by the county board of commissioners, and the appointment is for the unexpired term of the vacancy filled. A person holding any office either elective or appointive under any county adopting this act, or any of the townships of the county, or of this state, and a person not an elector of the county, is not eligible to hold the office of county auditor. No more than 2 members of any board of county auditors shall be affiliated with the same political party.
MCL 47.5