Mich. Comp. Laws § 397.305
Any county possessing a county library or any board of trustees of a regional library may enter into a contract with 1 or more counties, townships, villages, cities and/or other municipalities to secure to the residents of such municipality such library service as may be agreed upon, and the money received for the furnishing of such service shall be deposited to the credit of the library fund. Any municipality contracting for such library service shall have the power to levy a library tax in the same manner and amount as authorized in section 1 hereof for the purpose of paying therefor. Any municipality contracting for such library service may at any time establish a public library free for the use of its inhabitants, whereupon its contract for said service may be continued or terminated on such terms as may be agreed upon between the parties thereto.
MCL 397.305