Yes, in the state you title the car in which in your case is NH.
No, this is incorrect. Under MA law, you must pay 6.25 percent sales and use tax in MA regardless of where you plan to register the vehicle. You have 20 days in which to file the form and pay the tax if you're registering it anywhere other than in MA.
Failing to pay the sales and use tax on a MA purchase would be a criminal act.