(a) In the cities of Topeka, Salina and Hutchinson, Kansas, in which a free public library has been established as provided by law, in addition to the powers and duties conferred by law, the board of directors of the free public library shall prepare, publish and approve an annual budget for the maintenance and support of the free public library in the same manner as required by law applying to other taxing units and shall annually levy a tax not to exceed 2.5 mills on each dollar of the assessed tangible valuation of the property of such city for the maintenance and support of such free public library. Whenever the board of directors determines that the tax currently being levied by such board is insufficient to maintain and support the library and such board desires to increase the mill levy above the current levy, such board may adopt a resolution declaring it necessary to increase such annual levy in an amount which together with the amount of the current levy shall not exceed a total of four mills in any year.

(b) Whenever the board of directors of such free public library determines that the tax levy of four mills authorized by subsection (a) is insufficient to maintain and support the library, the board shall adopt a resolution declaring it necessary to increase the annual levy by an additional amount not to exceed 1/4 mill in any one year up to a total amount which shall not exceed an amount equal to six mills in any year.

(c) Any such resolution adopted under subsection (a) or (b) shall state the total amount of the tax to be levied for library purposes and shall be published once each week for two consecutive weeks in the official city newspaper. Whereupon such annual levy in an amount not to exceed the amount stated in the resolution may be made for the ensuing budget year and each successive budget year unless a petition requesting an election upon the proposition to increase the tax levy in excess of the current tax levy, signed by electors equal in number to not less than 5% of the electors who voted at the last preceding regular city election, as shown by the poll books, is filed with the county election officer within 60 days following the date of the last publication of the resolution. In the event a valid petition is filed, no such increased levy shall be made without such proposition having been submitted to and having been approved by a majority of the electors voting at an election called and held thereon. All such elections shall be called and held in the manner prescribed for the calling and holding of elections upon the question of the issuance of bonds under the general bond law. Such taxes shall be levied and collected in like manner as other taxes, which levy the clerk of such board of directors shall certify, on or before August 25 of each year, to the county clerk who is hereby authorized and required to place the same on the tax roll of the county to be collected by the county treasurer and paid over by the county treasurer to the treasurer of such board of directors.