| I live in Maine and bought my car in Mass...same as Texas said, I paid tax only to Maine. The dealership cut the Maine Department of Motor Vehicles a check for the tax amount when I closed on my car loan. Check with your state Motor Vehicle department & the finance person at your dealership to be sure how it works in your particular case...
I will say in Maine it was a pain in the butt because the state required that I buy a 1 day one-way transit plate and then register it the same day as I bought it (no 14 days when you buy it out of state)...it took a huge amount of running around, paperwork and waiting in line. | 
