Mich. Comp. Laws § 397.152
On completion of the survey of any proposed region, the proposal to establish a regional library shall be referred to the boards of supervisors of all counties included in such proposed region. The boards of supervisors shall act upon such proposal by resolution, and the votes of a majority of the members-elect of the board of supervisors in each of the counties included in the proposed region shall be necessary for the adoption of such proposal. In case of the rejection of such proposal by the boards of supervisors of any of the counties included in such proposed region, the plan may be altered in accordance with such action in order to provide for a regional library in such section of the state. The vote of a majority of the members-elect of the board of supervisors in each of the counties in such altered region shall be necessary for the adoption of such proposal.
MCL 397.152