Do you own your car if it is charged off?

No. The term "charge off" simply indicates that the creditor has decided to pursue other methods of collecting the debt owed. That could mean the debt will be sold to another party, the creditor could file a civil suit to collect the debt or other actions. Debts that are "charged off" remain valid and subject to collection unless they have been rendered invalid by the statute of limitations as determined under the laws of the debtor's state.