I was just going to ask the same thing.
I highly doubt you were arrested though. I had a similar situation in high school where we were brought to the police station for vandalism (we were toilet papering a rival high school), but none of us were ticketed or “arrested”. Our parents were called and we were sent home. I suspect the paper your dad signed was more about the police releasing custody back to him. I would think if you were actually arrested there would have been more legal processes to go through after that one night. But it seems like your dad would know best.