Ohio Rev. Code § 3375.213
Whenever a county library district has been created, or enlarged, under sections 3375.20, 3375.201, 3375.21, 3375.211, or 3375.212 of the Revised Code, all assets and liabilities of the former board of trustees of the library or libraries of the subdivisions which comprise said county library district shall become those of the county library district.
Any levies which the taxing authorities of such subdivision or of the former county library district have been authorized by the electors of the subdivision or of the former county library district to make for the payment of current expenses, interest, and retirement of bonds, or any other indebtedness of said boards of trustees shall thereafter be made upon the taxable property of all of the new or enlarged county library district and at such lesser rate as is necessary for the payment of such expenses, bonds, or indebtedness.
R.C. §3375.213