Mich. Comp. Laws § 38.701
The legislative body of any incorporated city of 250,000 or more (hereinafter referred to for the purposes of this act as the local legislative body), where free public libraries have been or may hereafter be established is hereby authorized, upon the application and recommendation of the local library board or commission or body duly authorized by law to maintain free public libraries in such city (hereinafter referred to for the purposes of this act as the library board), to establish a system of retiring allowances for the employes of such libraries which system shall be based upon the principle that there shall be accumulated, year by year, a reserve fund sufficient to provide the agreed annuity at the time of retirement. Upon the establishment of such system, the local legislative body shall raise by taxation each year a sum which will provide an adequate reserve fund.
MCL 38.701