The qualified voters of any locality whose governing body has not acted to create an authority under § 15.2-5102 may file with the governing body of such locality a petition asking the governing body to effect an agreement in accordance with § 15.2-5102 with the localities named in the petition. Such petition shall be signed by at least ten percent of the number of the locality’s voters who voted in the last presidential election and in no case be signed by fewer than fifty voters. The petition shall ask the governing body to petition the circuit court for a referendum on the question of the creation of the authority. If the governing body is unable, or for any reason fails, to perfect such agreement within three months of the day the petition was filed with such governing body, then the circuit court for the locality shall appoint a committee of five representative citizens of the locality to act for and in lieu of the governing body in perfecting the agreement and in petitioning for a referendum. The agreement shall not take effect unless approved in the referendum by a majority of the voters voting in the referendum.