Va. Code Ann. § 15.2-5431.6

If at the hearing, in the judgment of the governing body of the locality, substantial opposition is heard, the governing body may at its discretion petition the circuit court to order a referendum on the question of adopting or approving the ordinance, agreement or resolution. The provisions of § 24.2-684 shall govern the order for a referendum. If 10 percent of the qualified voters in a locality file a petition with the governing body at the hearing calling for a referendum, such governing body shall petition the circuit court to order a referendum in that locality as provided in this section.