
Quoting
free9man
If you were not arrested, then the most they probably did was file a report. That report is likely sitting in a drawer or a computer folder somewhere, depending on how long ago this occurred.
How in depth any given agency is when doing a background varies but it's not outside the realm of possibility that they might contact local law enforcement where you grew up to see if they had any run ins with you. If there is a report, it might come up. Depending on how long ago it is and your overall character since, it may or may not be an issue.