The governing body of any city or county upon petition of not less than fifty-one percent of the qualified electors of the city or county as determined by the total number of votes cast at the last general election or upon a majority vote of the qualified electors thereof voting on the question shall establish and maintain public library service within its geographic limits by means of a public library and reading room or other public library service, either singly or in cooperation with the state library, or with one or more cities or counties, or by participation in an approved state plan for rendering public library service under the Library Services and Construction Act [20 U.S.C. §§ 351-358], and acts amendatory thereof. Such question shall be submitted to the qualified electors upon resolution of the governing body or upon the petition of not less than twenty-five percent of that number of qualified electors of the city or county that voted at the last general election, filed with the governing body not less than ninety days before the next regular election. Library service may be discontinued within any city or county by any of the methods by which library services may be established, except that once established, such service shall not be discontinued until after it has been in operation for at least five years from the date of establishment.