Mich. Comp. Laws § 397.202

Sec. 2. (1) If a city council decides to establish and maintain a public library and reading room under this act, the mayor of that city shall, with the approval of the city council, appoint a governing board of 5 members for the library and reading room, chosen from the citizens at large, with reference to their fitness for that office. Not more than 1 member of the city council may be a member of the board at any 1 time. (2) If a city council decides, after the first appointment of the governing board under subsection (1), that the purposes of the library and reading room would be better served by a different number of members on the governing board, the city council may by ordinance change the number of members to an odd number not less than 5 or more than 9. (3) The term of office for each member of the governing board may be changed by ordinance to a term of not less than 2 years or more than 5 years. (4) Notwithstanding section 3, if the term of office is changed by ordinance by a city council, the term of office for subsequent appointments by the mayor shall be the same as prescribed by the ordinance.