If your dad signed papers relating to your questioning / detention by a police officer, then there may be a formal police record of the matter.
Arrests do not always involve the procedures outlined above by other posters. Thousands of cases have been dismissed or overturned due to improper arrest procedures which violated the detainee’s Constitutional rights.
You need to ask your dad about this incident.
If you ever apply for state bar clearance or for a security clearance, you may be required to disclose this incident.
P.S. Obviously you were a juvenile at the time of the incident so the local police dept. may have different procedures for infractions / minor offenses by juveniles such as releasing them to the custody of their parents. Was your father present at the scene ? Or did the officer detain you & transport you to your home ?