Mich. Comp. Laws § 397.301
The board of supervisors of any county shall have the power to establish a public library free for the use of the inhabitants of such county and they may contract for the use, for such purposes, of a public library already established within the county, with the body having control of such library, to furnish library service to the people of the county under such terms and conditions as may be stated in such contract. The amount agreed to be paid for such service under such contract and the amount which the board may appropriate for the purpose of establishing and maintaining a public library shall be a charge upon the county and the board may annually levy a tax on the taxable property of the county, to be levied and collected in like manner as other taxes in said county and paid to the county treasurer of said county and to be known as the library fund.
MCL 397.301