Michigan Compiled Laws, Chapter 397. Libraries § 397.195

Sec. 25. (1) A municipality other than a school district may become a party to an existing agreement if the agreement's requirements concerning the addition of a participating municipality are satisfied, or, in the absence of requirements in the agreement, if each of the following requirements is satisfied:

(2) If there is a districtwide library tax, the board shall condition acceptance of the municipality or portion of the territory of the municipality into the district on the authorization of that tax by a majority of the electors of the municipality or portion of the territory of the municipality voting on the proposal.

(3) Notwithstanding section 13  3 or a districtwide tax or taxes authorized by section 13, an existing district library agreement may change the number of mills authorized in the existing district library agreement if 1 or more municipalities or parts of municipalities join the existing district library district through a preexisting written agreement with the district library board. The change of the number of mills to be levied in the district library district shall be contingent on the approval by a majority of the voters of the existing district library district voting on the question and on the approval of a majority of the voters of each municipality or part of a municipality seeking to join the existing library district voting on the question. Defeat of the proposal submitted to the electors of the existing district library district shall not have any effect on the validity of the continued levy by the existing district library and district library board of previously authorized millage.