Ohio Rev. Code Ann. § 2725.20

If a prisoner brought before a judge under section 2725.12 of the Revised Code is in custody under a warrant or commitment in pursuance of law, the return of the writ of habeas corpus is prima-facie evidence of the cause of detention. If such prisoner is restrained of his liberty by alleged private authority, the return is only a plea of the facts therein set forth, and the party claiming the custody shall be held to make proof of such facts. Upon the final disposition of a case, the court or judge shall make such order as to costs as it requires.