(A)   When the Legislative Authority declares by resolution that an officer shall give a new bond, written notice shall be served by the Clerk upon the officer designated, and a copy of the notice, with a statement of the time and place of service, shall be recorded in the proceedings of the Legislative Authority.
   (B)   If the officer fails to give the new bond, with sureties, to the satisfaction of the Mayor, within ten days after such service, the Legislative Authority shall declare the office vacant, and the vacancy shall be filled in the manner provided in Title VII of the Ohio Revised Code.
   (C)   When a new bond is accepted or the Legislative Authority declares the office vacant, the sureties of the original bond shall cease to be liable for the acts of that officer done thereafter, but shall continue to be liable for his or her acts then already done.
(R.C. § 731.50)