From the facts you've provided above, my experience with identical situations indicates that your best chance for a good resolution to this issue will come from your open and ongoing communication with the bank about working something out. I've seen this before, and in each of the cases, there was a lot of room for negotiation with the bank.
Why? It's because the bank is in error, has given you the appearance of ownership of your car before satisfying your debt payment obligation before it was paid off, and the bank knows they need to work with you to resolve the situation.
I would advise a full and careful review of the documents you've signed before you contact the bank. I would be surprised if just because the bank erred you've been relieved of the requirement of full payment of the debt, even though the bank's actions indicated otherwise, and you got possession of the title early. But, I'd be equally surprised if you can't form a new agreement with the bank that will be beneficial for both of you.
In short, you probably don't have to sign the title back over to the bank, but you probably have to pay the debt in full. Otherwise, you could end up in a legal battle in which you end up paying all the legal costs of the costs of collection.
Good luck. Mark Arend
Let's say the situation is reversed. That is, for example, you already paid off the car but absentmindedly wrote the bank another check for $10000. Would you agree that the bank can keep your $10000?
"Isn't posses[s]ion 9/10 of the law?" There is no such law in the statutes or case law.
If you do not cooperate with the bank to correct a clerical mistake, the bank can easily go to court with your promissory note and payment history to show that you have not fully paid and get appropriate court orders.
Moreover, if you hide the car, that may turn into a criminal matter. A few years back, a guy in the WA area sent a product back to its manufacturer for a refund of less than $5. Instead, the manufacturer used his ZIP code as the payment amount. In WA, the ZIP codes are in the 98000-99000 range. The manufacturer eventually realized its mistake and contacted the guy to correct the mistake. The guy cashed the check with over $90000 and went into hiding. He was eventually found and charged with a crime.