Social security number, criminal database and finger prints are matched by the law enforcement agency. The officer who is in charge of records scans the fingerprints of the person in the computer and sees if they match.
Officers check for arrest records and outstanding warrants.
The more information you have about the person, the better it is.
You must know the full name of the individual as this is the foremost criteria.
Use the resources available on the Internet to check peoples criminal background who seems doubtful or is new to you and might work at your home or in office or for various other important reasons and clear your doubts and stay in peace.
Then, if you know about his/her birth date and the social security number of the person, it could help making the search easier for you.
However, remember that when you search on local and state government websites, you will get information of the crimes committed by that person in that state only.
On these websites you can search all kinds of records in all states so that they can get full information about the background of an employee.
This kind of information is very helpful for the employer.