One can file bankruptcy on anything except federally insured loans or guarantee. However the judge may make you liquidate your assets to help satisfy your debt.
You can file bankruptcy with any financial debt. Understand though that if the car is financed, the bank has a lien on the car and can repossess it for as part of the debt settlement.
You may file bankruptcy with any time of financing. Balloon financing on a car is no exception to the rule - you can still file bankruptcy if you cannot make the payments.
Do not file bankruptcy without giving up the car and having the debt fully detailed by the finance company. If you claim bankruptcy and reaffirm the car debt, you will be bankrupt but still behind on the car.