sales tax

No, not normally. If you do pay sales tax in the state you purchased the car, you may not have to pay it in your local area. Check with your state's Dept. of Motor vehicles to be certain.

Do you mean, if you purchased a vehicle in another State and bring it back to another State where you are registering it, do you have to pay Sales Tax in the State you bought the vehicle from? The usual rule is no - but you should check on this.