Typically, the spouse that retains the vehicle also assumes responsibility for the loan against it. If you're handling your case by consent order or marital settlement agreement, you'll want to make sure that responsibility for the loan is clearly distributed to your wife. If you've litigated your case through court and the judge awarded the car to your wife, you'll want to make sure the decree specifies that she will be responsible for the loan. In either instance, you should insist that she not only accept responsibility, but also refinance it into her own name. It's not in your best interests to have your name on a car loan for a vehicle you aren't driving.
If She Doesn't Refinance
If your wife doesn't or can't refinance the loan, you're still responsible to the creditor for the outstanding balance. Since the creditor isn't a party to your case or agreement, it can't be bound by the agreement. As such, ask the judge to order that if your wife doesn't, or is unable to, refinance the car by a certain date that she will then sell it and apply the proceeds to the loan. If you're settling your case by consent order or marital settlement agreement, make sure the same provision appears in your settlement documents.
Whether the car and loan is distributed by agreement or court decree, be sure to include a "hold harmless" provision with regards to the car loan. A "hold harmless" provision is an indemnification clause, requiring your wife to pay you back in the event that she fails to honor her obligation and the creditor comes after you for the money. This will make it easier for you to bring her back into family court to enforce the order. Furthermore, it can provide you with a layer of protection in the event your wife files bankruptcy.
In addition to having your name on the loan, you need to worry about your name remaining on the title. You could face a lawsuit if your wife has an accident in the car and your name is still on the title. Unless you want to undergo the expense of having to indefinitely maintain your own insurance policy on the vehicle, insist that your wife change the title as part of the terms regarding property division. Failure to address the title issue could end up costing you even more than the loan itself in the event of an accident.