It's not really a question of law, more of contract. Your contract will state that you are responsible for any damage done to the vehicle while in your care. The return receipt sets out in what state the car was when you returned it. Without this receipt you cannot insist that you didn't cause damage later claimed to have been yours. It's odd, because I usually receive an email receipt within a minute or two after dropping off the car. "You're all good to go, sir.."...buzz from my phone.