Ohio Revised Code Title VII. Municipal Corporations § 735.23

No streets or alleys, except those laid out on a plan made by the platting commissioner pursuant to sections 735.19 to 735.22, inclusive, of the Revised Code, shall subsequently be in any way accepted as public streets or alleys by the city, nor shall any of the public funds be expended in the improvement or repair of streets or alleys subsequently laid out and not on such plat, but any city may exercise the power of condemnation in any case in which it may condemn and appropriate property to public use, although it is not shown as a street on such plat.