Ohio Rev. Code § 1901.027
In addition to the territorial jurisdiction conferred by section 1901.02 of the Revised Code, the municipal courts established in Athens, Batavia, Gallipolis, Georgetown, Cincinnati, Ironton, Chesapeake, Marietta, Portsmouth, and Steubenville and the municipal court established within Columbiana county that is described in division (C) of section 1901.01 of the Revised Code have jurisdiction beyond the north or northwest shore of the Ohio river extending to the opposite shore line, between the extended boundary lines of any adjacent municipal courts or adjacent county courts. Each of the municipal courts that is given jurisdiction on the Ohio river by this section has concurrent jurisdiction on the Ohio river with any adjacent municipal courts or adjacent county courts that border on that river and with any court of Kentucky or of West Virginia that borders on the Ohio river and that has jurisdiction on the Ohio river under the law of Kentucky or the law of West Virginia, whichever is applicable, or under federal law.
R.C. § 1901.027