Can my parents be sued if I was driving their car?

I am a lawyer in CT and practice in this area of the law.  The law in most states is that the owner of the car (and their insurance policy) is on the hook when they let someone else driver the car.  since you were on your parents insurance you are covered under the policy.  therefore, you and your parents need to forward the claim/lawsuit to your insurance carrier as they have a duty to defend you and pay the plaintiff up to the amount of the insurance policy.  If the policy does not cover the damages, your parents may be personally liable for the balance.