Mich. Comp. Laws § 397.31

Sec. 1. As used in this act: (a) "Public library" means a library, the whole interests of which belong to the general public, lawfully established for free public purposes by any 1 or more counties, cities, townships, villages, school districts or other local governments or any combination thereof, or by any general or local act, but shall not include a special library such as a professional or technical library or a school library. (b) "Qualified public library" means any public library which is open to and available to the public at least 10 hours per week or any library which has a contract with a public library board to furnish library services to the public.