Impossible to answer, with out naming specific states. Some states require sales tax to be paid at time of purchase, regardless of where the car is registered/home state of the buyer. In all cases I know of, the only way to get out of paying the tax to the pruchasing state is to have the car delivered to you out of the purchasing state. Usually a well-documented paper trail is required (trucking bills of lading, etc).
Other states only charge the sales tax at time of registration. Out of state buyers who are registering the car in their home state do not pay sales tax to the dealer's home state.
Specific states I am familiar with:
First group (paid at purchase) - MA, CA
Second group (paid at registration) - VT
I've bought cars in MA, brought in CT plates, and driven home. Paid 5% to MA, and then 3% to CT (CT sales tax was 8%, but they grant a credit for sales tax paid at purchase).
I bought a car in VT and registered in NH. No sales tax, period. Several VT dealers near the NH and MA state lines routinely advertise "pay no extra tax to VT - out of state buyers are exempt from VT tax"
But Tesla can/should deliver the car to your home, and there's no such thing as a low-priced out of state dealer, so this should all be moot, right?
Most states that have sales tax charge the difference between what you paid at purchase time and locally if it's a positive value. Others have exclusions if it was used out of state for some period of time. Which makes an interesting question as here in Washington for the next year no sales tax on electric vehicles.
So if you want to buy a Tesla and have some body in Washington use it for year I am your man (grin).
Seriously check around with your buds; somebody is bound to know a CPA in your state who can give you a better answer.
With my Tesla buying experience: I bought the car online. I live in Wisconsin. The car was delivered to the Chicago SC in Illinois where I picked it up. I paid no sales tax when I picked up the car. I received a 30 day Illinois temp license plate when I picked it up. I paid Wisconsin sales tax when I registered the car in Wisconsin and received my official license plate.