Ohio Rev. Code Ann. § 3111.39

If more than one child support enforcement agency receives a request to determine the existence or nonexistence of a parent and child relationship concerning the same child and each agency is an appropriate agency for the filing of the request as provided in section 3111.38 of the Revised Code, the agency that receives the request first shall act on the request. If an agency that receives a request is not the appropriate agency for the filing of the request, the agency shall forward the request to the agency of the county in which the child or the guardian or legal custodian of the child resides, and the latter agency shall proceed with the request.