The registered voters of any such county, city, or town may, by petition filed with the circuit court thereof, ask that a referendum be held on the question of whether the members of the school board of the county, city, or town shall be elected directly by the voters. The petition shall be signed by registered voters equal in number to at least 10 percent of the number registered in such locality on the January 1 preceding its filing. Upon the filing of a petition, the circuit court shall order and require the election officials at the next general election to open the polls and take the sense of the voters therein on that question. The petition shall be filed with the court not less than 111 days prior to the general election. The clerk of the court shall cause notice of the referendum to be published once a week for the three consecutive weeks prior to the referendum in a newspaper having general circulation in the county, city, or town, and a copy of the notice shall be posted during the same time on the door of the courthouse of the county or city, or of the county within which the town is located. The question on the ballot shall be: “Shall the method of selecting the school board be changed from appointment by the governing body (or the school board selection commission, whichever is applicable) to direct election by the voters? [ ] YES [ ] NO” The election shall be held and the results certified as provided in § 24.2-684.