Bought a vehicle out of state, can I get the tax back since I am not a resident of that state?

No, sales taxes are payable at the point of sale and there are no states that refunds it if paid to another state.  Many states that have a sales tax also have a use tax that would apply if you did not pay sales tax when the purchase was made if the car is used in the state.

This is an income tax forum.  You'll probably not find an answer here.  When you register the vehicle in you home state, they may give you a credit for the tax paid in the other state (or waive the home state use/sales tax because you paid in the other state).  If you paid in both states, you could contact  the original state about a refund.  If you live in a state with no sales tax  (Alaska, Delaware, Montana, New Hampshire, and Oregon) you probably cannot get a refund.