You will probably see a tax bill at some time then so don't be surprised. Below is a snapshot of the DMV form that you would have needed to complete to legally not pay taxes on your vehicle purchase. These are the only acceptable instances where you would not have to pay tax on a used car, no matter if you purchased it from a dealer or private party.
You also may want to ensure all of the paperwork was done correctly as there would be more than one fee the DMV would charge. I could be wrong, but only paying $39 in DMV Fees doesn't seem right when buying a used car in CA. You would have the title transfer fee and registration transfer fees at a minimum.
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