Va. Code § 15.2-5105
If at the hearing, in the judgment of the governing body of the participating 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. When two or more localities are participating in the formation of such authority, the referendum, if ordered, shall be held on the same date in all participating localities. If ten 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.
Va. Code § 15.2-5105