(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:

    (a) The legislative body of the municipality resolves by majority vote that the municipality become a participating municipality and that all or, pursuant to section 3(2), a portion of the territory of the municipality be added to the district.

    (b) The resolution is conditioned upon the board‘s adopting, within a period of time specified in the resolution, amendments to the agreement specified in the resolution. The amendments specified shall reflect the addition of the municipality or of the territory to the district and shall include, but need not be limited to, changes in board representation or the percentage of funds necessary for the establishment and operation of the district library to be supplied by each participating municipality after the municipality becomes a party to the agreement.

    (c) The board amends the agreement within the time and in the manner specified in the resolution of the legislative body of the municipality. Notwithstanding anything to the contrary in the procedure for amending the agreement set forth in the agreement pursuant to section 4, the amendment shall be made by majority vote of the members of the board elected or appointed and serving.

    (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 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.