Ohio Rev. Code § 1341.12
Upon notice being given by a surety of his unwillingness to continue as surety of a constable or marshal, the board of township trustees or legislative authority of the municipal corporation shall immediately inform such constable or marshal, in writing, of the refusal of his surety to continue as such, and that he is required to give a new bond conditioned according to law. If such constable or marshal gives such bond to the satisfaction of the board or legislative authority, within ten days after receiving notice, the sureties upon the first bond shall be released from further liability thereon. If the constable or marshal fails to give a new bond within ten days after receiving such notice, such failure shall be deemed a resignation of his office, and the board or legislative authority shall proceed to fill such vacancy as in other cases.
R.C. §1341.12