Mich. Comp. Laws § 62.13
A vacancy occurring in the office of president, trustee, or any other elective office shall be filled by appointment by the council, and the appointee shall hold office until the next regular village election. All vacancies in any other office shall be filled by the president, by and with the consent of the council. If by reason of removal, death, resignation, or otherwise, the membership of the council is reduced to less than a quorum, the remaining council members shall call a special election for the purpose of filling all vacancies in the office of trustee, if a petition signed by not less than 10% of the qualified voters of the village is filed with the village clerk within 10 days after the vacancy or vacancies occur. If a petition is not filed within the time stated, then the remaining council members may either call a special election, or may appoint a sufficient number of trustees to constitute with the members in office a quorum of the council, who shall then fill the remaining vacancies as provided in this section. If all the officers and trustees of a village have died or moved from the village, and no successors have been elected or appointed to fill the vacancies, the township clerk of the township within which the village is situated shall, upon petition of 10% of the qualified voters residing in the village, call a special election for the election of the officers and trustees of the village to be held on a regular election date as established under section 641 of the Michigan election law, 1954 PA 116, MCL 168.641. The township shall perform all of the other duties with respect to the election as the village might have done had the vacancies not existed, including the preparation of ballots, the appointment of election inspectors, the counting and canvassing of the ballots, and the certification of the persons elected to the offices for which the election was held. The expenses of the election shall be paid by the village as provided in section 642 of the Michigan election law, 1954 PA 116, MCL 168.642.
MCL 62.13