Amy is absolutely correct here. Find out what you can.
The internet is a wonderful resource for getting background info on a person. You can find out if he has a criminal record through local court websites or you can pay a fee for one of the background check services on the net (helps if you want to check a wider range such as statewide as opposed to local).
If he does have a criminal record you can write to the arresting police department and get a copy of the actual police report. It's all covered by the Freedom of Information Act.
It should be obvious by now that I have had some experience in this area. In my case, OM #2 had a history of domestic violence. They were all against male members that he was living with but it showed a violent history.
When I confronted my wife with the info, I matter of factly told her that I would investigate anyone that would be involved with my kids. I kept it to being about safety for my kids which diffused any thought on her part about me being vindictive.