Ohio Rev. Code § 709.37
Any two adjoining municipal corporations may, by ordinance of their respective legislative authorities, agree to a change in the boundary line separating such municipal corporations, provided such change does not involve the transfer of territory, inhabited by more than five voters, from one to the other or from each to the other. The ordinances setting forth such agreement shall be certified to the board of county commissioners. Upon receipt of such certified ordinances, the board shall proceed by resolution to approve such change of boundary and to make such adjustment of funds, unpaid taxes, claims, indebtedness, and other fiscal matters as the board determines to be proper. Transcripts of the ordinances, agreement, and resolution certified by the board shall be filed in the office of the secretary of state and shall also be filed and recorded in the office of the county recorder. All fees and costs for such filing and recording shall be assumed and paid by such municipal corporations in such proportions as the board determines.
R.C. §709.37