When I bought my car I wrote two checks. One to the dealer For the car, and another one to the state for the tax, even though the dealer was the one sending in the paperwork and my tax check. Why did I write a separate check to the state? Because if a dealer goes belly up between the time you give them a payment and the tax is sent in, then you're left with a vehicwe that has not had taxes paid, and you have to write another check to the state before you can get a license plate for it. A check written to the state can not be cashed by the dealer.
Don't laugh it has happened to people years ago. People had to pay the tax twice, then wait for whatever little they could get back from what was left of the dealer. Fortunately for me I wasn't one of them.