In any county in which there has been created a county library district, the taxing authority of any subdivision of the county not inincluded in said library district and maintaining a free public library for the inhabitants thereof may, upon request of the board of trustees of said free public library, adopt a resolution providing for the inclusion of said subdivision in said library district. Upon the adoption of such a resolution, the taxing authority of the subdivision and the board of trustees of the free public library shall take appropriate action transferring all title and interest in all property, both real and personal, in the name of said free public library to the board of trustees of the county library district. Upon the transfer of such title and interest in such property said subdivision shall become part of the county library district.