Mich. Comp. Laws § 397.401

Sec. 1. The territory over which the library commission in any city having a population of more than 250,000 shall conduct the activities to it by law confided, and to which shall apply charges and obligations heretofore or hereafter imposed for the purposes of any said commission, shall be co-extensive with the boundaries of any said city and shall automatically change by and with any change in said boundaries.