We had issues with this with DD's application years ago, but I am sure solutions vary from state to state, county to county, municipality to municipally, desk officer to desk officer.
Really you don't need alot of direction to resolve this. The answer is: When working with ANY government organization you NEVER accept the first "No"; "I don't know"; not "my problem" or an absurd additional form/input/requirement in order to act on your request.
If the school resource officer won't handle it, make a call to your local police station, If they don't help you, call City Hall info desk and ask for help.
Never get angry, just ask for help; If you get an "I don't know," you always ask for a referral to a person or resource who does know, or can get you closer to someone who does know. Its not your job to ask EXACTLY the right questiion.
Never denigrate the last person you called who wouldn't help. Just "Hi, I have been accepted to the USNA They need a copy of my police records, I've called X, Y, Z and I can't seem to get this done; can you help me?" Trust me, with that pitch someone will make an effort to help you, you just have to work the chain.
Note to STEM types: for this kinda stuff knowing the "right answer" is great; learning how to work your way up a government "responsibility-chain" and understanding they are supposed to help you is priceless. I'm quessing your issue resolves in 2-3 phone calls.
Just my put: Congratulations!