Mich. Comp. Laws § 397.287

Sec. 7. Bonds issued pursuant to this act are debt of the district library and not of the participating municipalities. If a participating municipality withdraws from a district library, taxes imposed for payment of bonds approved as provided in this act before the adoption of the resolution to withdraw shall continue to be levied within the district as if the municipality did not withdraw from the district library until the principal of and interest on those bonds are paid in full.