As the 4.15% motor vehicle Sales and Use Tax (SUT) in VA is only paid when a vehicle is sold or the ownership of the vehicle changes hands; it, unfortunately, is not deductible. When a vehicle tax is assessed annually on the value of the vehicle, that tax can be deductible.
This is not entirely accurate. If you itemize you have a choice of deducting state income tax or general sales tax. You can add the motor vehicle sales tax to the general sales tax you compute on the IRS web site. If it is larger than the state income tax you would want to use the general sales tax. In fact if it is relatively close you still might want to use it since state income tax is not deductible on the Virginia return but general sales tax is. If close, try it both ways and see which one provides the best combined Virginia and Federal result.
If you decide to use the general sales tax your state refund will not be taxable the following year. If you decide to use the state income tax be sure to include the motor vehicle sales tax on the state refund worksheet the following year.