(1) Any city of the first class may, by ordinance, establish and maintain within its corporate limits a free public library, with circulating and reference departments and reading rooms, or any of them, for the use of the residents thereof, with such branches and stations as the board of trustees of the library think proper. All the uses and privileges of such library shall be free and equal to all residents of the city, subject only to the rules and regulations established by the board of trustees. The board may extend the privilege and use of the library to persons residing outside of the city, upon such terms and conditions as the board prescribes.
(2) The city legislative body may pass such ordinances as the board recommends providing for the punishment of persons injuring the library property and regulating the conduct of persons using the library.