Unfortunately you are going to have to deal with the car in your filing. All assets must be listed or your petition is subject to dismissal, and you are subject to perjury in a Federal Court.
If the cars are paid off, and you are the legal owner both cars must be listed and both are subject to liquidation by the Trustee. It doesn't mean it will be attached but it is subject to it. If the car is worth a few thousand dollars they would order the car sold and take the proceeds.
In fact, at this point you cannot transfer the car into his name even if you wanted too. A person has to disclose any transfer of property up to one year prior to filing bankruptcy. If you have transfered property they will inquire further and could order the transfer void and bring back the asset into the bankruptcy.
The Court does not search your assets typically, although they can request any documentation they deem propert until discharged. They will ask you if you have disclosed all your assets on your schedules, and if you have transfered property in the 341 meeting, you are under oath in Federal Court, so you must be truthful.
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