The governing body of any county or tier-city may, by ordinance passed by a recorded affirmative vote of a majority of the members thereof, petition the circuit court for the county for an order declaring the county or tier-city totally or partially immune, as the case may be, from city-initiated annexation and from the incorporation of new cities within its boundaries. If the petition for total or partial county immunity is filed after the institution of a proceeding for city-initiated annexation of county or tier-city territory or for the incorporation of a new city within the county’s or tier-city’s boundaries under the provisions of Chapters 32 (§ 15.2-3200 et seq.) or 38 (§ 15.2-3800 et seq.) and before the time limit for pleadings established by the court pursuant to § 15.2-3204 or § 15.2-3805, the proceeding for annexation or incorporation shall be stayed until the court determines the question of total or partial county immunity. The clerk of the circuit court shall give notice of its receipt of a county’s or tier-city’s petition for immunity to each court in which the county or tier-city may be a party to a city-initiated annexation proceeding or to a proceeding for the incorporation of a new city.