If a dealership assigns a car to a finance company and the finance company says you don't owe them can the dealer repossess?

If the finance company has been paid in full, then why would the dealership (or the finance company) want to repossess your car?

If the loan hasn't been repaid and is long overdue, then the dealer and finance company will probably decide who actually repossesses the car. Either way, it's up to them, not you.

Best thing to do is check the fine print in your loan agreement (which you signed when you bought the car) and see what it says about overdue payments, repossession, etc. If you've lost it, call your dealer and ask for a copy.