The governing body of any county may, by ordinance passed by a recorded majority vote of all the members thereof, petition the circuit court for the county, alleging that the county meets the criteria set out in § 15.2-3907, for an order declaring the county eligible for city status. The circuit court with which the petition is filed shall notify the Supreme Court, which shall appoint a special court to hear the case as prescribed by Chapter 30 (§ 15.2-3000 et seq.) of this title.