Michigan Compiled Laws, Chapter 397. Libraries § 397.178

Sec. 8. (1) An individual appointed as a board member shall be a qualified elector of the participating municipality that appoints the member on the date the appointment is made. A candidate for election as a board member shall be a qualified elector of a participating municipality on the deadline for filing nominating petitions. A candidate for appointment or election shall be a resident of the district.

(2) The office of board member becomes vacant when the incumbent dies, resigns, is convicted of a felony, is removed from office by the governor pursuant to section 10 of article V of the state constitution of 1963, or ceases to be a resident of the district. In addition, the office of an appointed board member becomes vacant when the incumbent ceases to be a resident of the participating municipality that appointed the incumbent.