Mich. Comp. Laws § 85.16: Office declared vacant; failure to file oath or bond.

Sec. 16.

If any person elected or appointed to office shall fail to take and file the oath of office, or shall fail to give the bond or security required for the due performance of the duties of his office, within the time herein limited therefor, the council may declare the office vacant, unless previous thereto he shall file the oath and give the requisite bond or security.