Yes, you can potentially claim the sales tax. If you are able to claim the sales tax, it would not decrease your state refund.
If you have filed your return already, you would need to file an amendment (you can find the instructions at the bottom of this answer). When you begin your amendment, you would want to enter that sales tax information using the directions below. TurboTax will help you to decide whether to deduct your sales tax paid or local/state income taxes paid (usually from your paycheck), if you are able to itemize your deductions.
After you enter the information, if the amount of your refund does not change, then you do not have to mail anything an and you are done.
To enter the sales tax paid when you purchased your vehicle, you can follow the steps below:
Type Sales tax car in the Search box and Select the same phrase in the drop down box
Select Jump to and you will be taken to the sales tax section
Select Continue with Sales Tax then Easy Guide
Enter your state and tax rate or Edit it if you have already entered it.
After finishing that you will see a Major Purchases screen, you should select Yes you did buy major items
You can then enter your car sales tax paid on the Enter Major Purchases screen
The directions to start your amendment are below: