If the vehicle was purchased while they were married, ownership of this vehicle should be determined by the divorce agreement. That person will be responsible for insuring it. Now, if the vehicle belongs to the ex-husband, the ex-wife can also be held accountable for the insurance coverage at the time of the accident - if she is the driver. So, if the vehicle belongs to the ex-husband, and he is unable to insure it (because he lives out-of-state) and she will be driving it, she will need to insure it - even though she technically does not have any "insurable interest" in the vehicle. Now, you can follow this link to learn more about your state's Department of Insurance to learn their rules of insurance coverage.