What is the religious ruling on swearing an oath to prove the loss of a receipt pertaining to a car, when official authorities request this for the renewal of its license?

If you are certain that the receipt was lost by the previous owners, then there is no sin in swearing before the court that it was lost, based on their statement. Whoever swears an oath about something they believe to be true incurs no sin initially, and no expiation is required of them if it later becomes clear that they were mistaken. It is preferable for the previous owners to swear the oath, if possible.