You do not own the car, so you are not on title for it, so, No, you don’t have to list it as one of your personal assets. However, you are required to list it in the Statement of Financial Affairs as property that someone else owns that you are borrowing.
At the 341 Meeting of Creditors, the bankruptcy trustee will ask you what you are using for transportation. His follow-up question will then be, “Do you have any ownership interest in the vehicle?” It’s not a scary question, but it’s nice to be prepared and be able to answer that it is not yours.
What is a little more involved is when your parents have purchase a car, in their names, and have a loan against it with their bank or credit union. You are making the payments on it, but everything is in their name. In this kind of situation, we let the trustee know that you are making the payments and that, yes, one day you hope to own it. We don’t try to hide anything from the bankruptcy trustee.