Check your insurance. There might be a clause to preclude it. If not. yes, you still owe. Best in this case to face your financier , come to an agreement. Bring all paperwork.
EDIT: Make sure tower followed the law, too. You might want to talk to free legal aide. If they did not cross all tees and dot all i's, sue the tower, first. My car was illegally towed; it had been legally parked. I fought over the tow fee, storage fee ( 24 hours later, $150.) I had to file against the cops, in my case., Tower was just following orders.