There are no free criminal background check sites. The sites which they claim are free are actually bogus. There are some that allow you to search and give you vague details of the person. Afterwards, if you are satisfied, you can pay and get the whole search results.
You can search if they have a sexual offense that is public record because sex offenders have to register with the police dept. in the city they live in. Other than that you have to pay to get other information.