if someone gave me the keys to a car that was not there and I caused damage to the car who is responsible

If you are responsible for causing property damage, then you are responsible for the cost to repair that damage.  Ownership is not the issue; the issue is one of liability.  The person who knowingly gave you the keys to someone else's car may also bear liability.  The actual owner can collect from either or both persons. Note too that the failure to pay for damages -- apparently caused in a car crash -- can also result in the suspension of your driver's license.  The cost to then reinstate the license could be hundreds of dollars.