Sec. 2. In cities and incorporated towns, a governing body may establish a free public library in connection with the common schools for:
(1) the care, protection, and operation of the library;
(2) the care of books and other materials; and
(3) borrowing and returning books and other materials and penalties for any violations.
However, in any city or incorporated town where there is established a library open to all the people, a tax may not be levied.