Such ordinance shall also provide for relief from tax and a refund of the appropriate amount of tax already paid, which shall be prorated on a monthly basis, where any motor vehicle, trailer, semitrailer, or boat loses its situs within such locality after the tax day or after the day on which it acquires a situs (hereafter "situs day"). No refund shall be made if the motor vehicle, trailer, semitrailer, or boat acquires a situs within the Commonwealth in a nonprorating locality. When any person sells or otherwise transfers title to a motor vehicle, trailer, semitrailer, or boat with a situs in the locality after the tax day or situs day, the tax shall be relieved, prorated on a monthly basis, and the appropriate amount of tax already paid shall be (i) refunded or (ii) credited against the tax due on any motor vehicle, trailer, semitrailer, or boat owned by the taxpayer during the same tax year by the treasurer of such locality. Such refund shall be made within thirty days of the date such tax is relieved. No refund of less than five dollars shall be issued to a taxpayer, unless specifically requested by the taxpayer. When any person, after the tax day or situs day, acquires a motor vehicle, trailer, semitrailer, or boat with a situs in the locality, the tax shall be assessed on the motor vehicle, trailer, or boat for the portion of the tax year during which the new owner owns the motor vehicle, trailer, semitrailer, or boat and it has a situs within the locality.
Any person who moves from a nonprorating locality to a prorating locality in a single tax year shall be entitled to a property tax credit in the prorating jurisdiction if (a) the person was liable for personal property taxes on a motor vehicle and has paid those taxes to a nonprorating locality and (b) the owner replaces for any reason the original vehicle upon which taxes are due to the nonprorating locality for the same tax year. The prorating locality shall provide a credit against the total tax due on the replacement vehicle in an amount equal to the tax paid to the nonprorating locality for the period of time commencing with the disposition of the original vehicle and continuing through the close of the tax year in which the owner incurred tax liability to the nonprorating locality for the original vehicle.
Va. Code § 58.1-3516