Any one or more cities of the third class is hereby authorized to join with any one or more townships or portions of one or more townships in one or more counties in the creation of a library district, upon the presentation to the board of county commissioners, of the county in which such proposed library district is located, of a petition setting forth the boundaries of the proposed library district and requesting the formation of such library district. Such petition shall be signed by not less than ten percent (10%) of the qualified electors of said proposed district who reside outside the limits of the incorporated city, and a like petition signed by not less than ten percent (10%) of the qualified electors who reside within the corporate limits of a city of the third class within said proposed district. The sufficiency of such petition to be determined by the board of county commissioners, determined upon the basis of the total vote cast for secretary of state in the last preceding general election within said city of the third class and within the boundaries of said proposed district of the township or portions of townships comprised within the proposed boundaries of said library district; and in the event a portion of any township is within such proposed boundaries, the total vote cast for secretary of state in said township shall be used. If the city of the third class within the boundaries of said library district owns and is operating a library at the time said petitions are filed, said petitions shall be accompanied by a copy of a resolution adopted by the governing body of said city of the third class within such district; such resolution shall state that said city of the third class agrees, upon the creation of the proposed library district, to convey, assign and transfer to said library district all books, equipment, moneys, endowment funds and all other assets of said city library, to and for the use of said proposed library district. The governing body of such city of the third class located within said library district is hereby authorized to adopt such a resolution, and upon the creation of said library district by the board of county commissioners the governing body of such city, in conformity with such resolution, is hereby authorized to make and execute the necessary assignments and conveyances to transfer to such library district all property and assets of said city library. The board of county commissioners of the county in which such proposed library district is located shall, at its next regular meeting following the filing of such petition, examine said petition and determine its sufficiency. If the board finds that said petition is regular and in due form, as herein provided, it shall cause to be submitted to the voters of such proposed district, at a special election called for the purpose of voting upon the question, the establishment and maintenance of a library by such proposed library district. A notice of such election shall be given by publication of such notice in a newspaper having general circulation within the boundaries of such proposed district. Said notice of election shall be published in two successive issues of such newspaper and such election shall be held within seven (7) days after the last publication of such notice. Such notice of election shall be signed by the board of county commissioners and such election shall be conducted by and under the supervision of the county clerk of said county in the manner provided by law for the conduct of general elections. The county clerk shall determine the number of voting precincts needed within such proposed district, at least one of which precincts shall be in the corporate limits of the third-class city in said proposed library district, and shall designate and appoint the election board, or boards, to serve at the voting precinct or precincts within such proposed library district.