Ohio Rev. Code § 1703.25
If any fees required to be paid under sections 1703.01 to 1703.31, inclusive, of the Revised Code, are paid under protest, if an action to recover such fees would lie against the secretary of state while they were held by him, and if such fees are paid into the state treasury in compliance with section 111.18 of the Revised Code, then actions to recover such fees shall be brought against the state and not against the secretary of state. For such purposes permission is hereby given to bring and maintain actions against the state to the extent that such actions might be brought and maintained against the secretary of state if the fees were held by him. Service of process in such actions shall be made on the attorney general, who shall represent the state.
R.C. §1703.25