This happened to me. I bought a boat from Hardin Marine, they took my SeaDoo in on trade. They did not register the SeaDoo until after the new year (I traded in June). Because they went out of business soon after I was stuck with a $60.00 Property Tax bill that wasn' t mine. We tried to reason with the tax collector but they didn't want to hear it, and since we had no legal change of ownership until after the 1st of the year, the bill became mine. They put a tax lien on my house for $60.00 and I'm still having to splain that every time I try to use my credit.
If you have sold it or traded it in, keep you bill of sale and immediately notify the county assesors office of the change of ownership. If you don't you'll get the bill, and good luck trying to get them to change it afterwards.