Any city, town or county shall have the power to enter into contracts with adjacent cities, counties, towns, or public institutions of higher education to receive or to provide library service on such terms and conditions as shall be mutually acceptable, or they may contract for a library service with a library not owned by a public corporation but maintained for free public use. The board of trustees of a free public library may enter into contracts with county, city or town school boards and boards of school trustees to provide library service for schools. Any city or county governing body contracting for library service shall, as a part of such contract, have the power to appoint at least one member to the board of trustees or other governing body of the library contracting to provide such service. Any city or county thus contracting for library service shall be entitled to the rights and benefits of regional free library systems established in accordance with the provisions of § 42.1-37. The board of trustees or other governing body of any library established under the provisions of § 42.1-33 may also, with the approval of and on terms satisfactory to the State Library Board, extend its services to persons in adjacent areas of other states.