The governing body of any locality may adopt ordinances requiring that dogs within any such locality be kept on a leash or otherwise restrained and may, by resolution directed to the circuit court, request the court to order a referendum as to whether any such ordinance so adopted shall become effective. Such referendum shall be held and conducted, and the results thereof ascertained and certified in accordance with § 24.2-684. The court shall require the governing body to give appropriate notice of the time, place and subject matter of such referendum. The results of the referendum shall not be binding upon the governing body of the locality but may be used in ascertaining the sense of the voters.