What is the ruling regarding someone who doubts whether he caused a scratch on another person's car, given that he heard a sound and is unsure of the source of the scratch?

Rights are only established as obligations (in one's conscience/responsibility) through certainty or a strong presumption, and the fundamental principle is the acquittal of responsibility. So, if what the questioner mentioned is merely a doubt, then nothing is obligatory due to it. However, if it is a strong presumption, then he must investigate and search for the owner of the right or seek his forgiveness, because legal rulings are based on strong presumptions.