Below citation and website are for your information. It is from the Fairfax county in Va. Therefore, if you notify the county you were in, you should be able to get your account adjusted and refund should be due to you. Also, you should have notified the DMV the sale of your vehicle.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP
What should I do if I have sold my vehicle or moved my vehicle out of Fairfax County?
In Fairfax County, the car tax on motor vehicles (cars, trucks, motorcycles, and vans) is prorated to reflect the time the vehicle was normally garaged in the County. To ensure that your motor vehicle is taxed accurately, you must notify the County when a vehicle is moved out of the County or sold. This may be done in person by visiting our office, by telephone, or by email. You may also report vehicle sales or moves online using our vehicle update tool.
If you have sold your vehicle or moved the vehicle out of the County, the following information is required: property owner name and daytime phone number; vehicle identification number (VIN), year, make, and model or Fairfax County property number (if known); and date the vehicle was sold or relocated. If the vehicle was moved out of the County, you must also provide the new address.
Upon notification that a property has been moved or sold, the Department of Tax Administration will adjust your account.
Please note that vehicles which are moved out of Fairfax County to a non-prorating Virginia jurisdiction during the tax year are not prorated. Effective July 1, 1998, vehicles registered in Virginia but normally kept out of state are also taxable by the jurisdiction where registered.