Ohio Rev. Code § 3375.403
The board of library trustees or governing body of any public library may contract for public library service with the board of library trustees or governing body of one or more libraries within the state that serve the general public, public or private schools, colleges, or universities, or a profession, occupation, or business. The board of library trustees of any public library may contract with boards of education of school districts within its territory to provide school library service, the boards of education paying all or part of the expense thereof.
Contracts as provided in this section may be terminated by mutual agreement, or by either of the two contracting parties on giving six months' notice before the day upon which taxes upon real estate become a lien.
R.C. §3375.403