As far as I know, if you bought a car, you are responsible for paying the tax directly to the state. It isn't the same as buying a CD at Best Buy because there are so many other facets to cars, like boats. There is Sales tax 1 time, perosnal property tax every year (depending on state), registration every year.
As far as documentation goes, different states have different laws. From reading here on OSO, I have come to understand that many states still require full taxes and a registration sticker even though the vessel is documented with the coast guard. They may not require hull numbers though. I would bet that you are liable for all taxes that have not yet been paid. The theme here? Don't get between a government entity and its tax collections!!