Go to a main police station in your city (the one with more than 20 computers, not the one with only two poclicemen sitting inside). Tell them that you are going to hire a over-night baby sitter for a period of time, you want to do a criminal record check. what is the procedure,
They will tell you that you have to have a written agreement from that person. They will give you the form. go home and fill it , let your son sign it. Let Your son drop it to the police station with his ID. He will pay $25. After 2-4 weeks, the police will phone your son or you to pickup the result.
You might save the $25, if you know an email address of the police station. If you have luck, some nice policeman will do a search in his fingertip and reply you in email in one day. (Certainly he broke the law without ask for your ID, but there are cases people are so nice that go out of their way to help). I met that kind of good policeman once.
The search result might have your son's name in it. Do not panic. He might be a person with the same names. Do a second search with your son's finger print. That will cost more than $100.