Be concerned about personal security whenever you hire a nanny or other household help. For a modest fee, you can get credit, driving, and employment checks while finding out if applicants have criminal records. You likely will want to avoid hiring someone with a history of drunk driving, for example.
A release must be obtained in order to look into someone’s background but you shouldn’t hire someone who won’t sign a release. It’s your house and your kids so you should check. In practice, you probably won’t lose out on any highly qualified employees because you ask for these releases.
Where can you go for such background checks? One approach is to contact the nearest FBI office. You’ll probably get leads to former agents who do this type of work; be sure to ask about fees, because they can vary widely.