Ohio Rev. Code § 709.34: Government of the municipal corporations.

When the annexation of a municipal corporation under sections 709.23 to 709.33, inclusive, of the Revised Code, is completed, the two former municipal corporations shall be governed as one, embracing the territory of both, and the inhabitants of all such territory shall have equal rights and privileges, subject to the conditions of annexation. The annexation shall not affect any rights or liabilities existing at the time of annexation, either in favor of or against such municipal corporations, except such as are affected by the conditions of annexation. Actions founded on such rights and privileges may be commenced, and pending actions prosecuted to final judgment and execution, as though the annexation had not taken place.