Background Checks without SS Number

[Cole Davis]

A prospective tenant with (great credit / clean background) of ours has a roommate that is here on a work permit. He has a Tax ID number but no Social Security number. Our current tenant screening company can only search criminal records by SS#. 

Has anyone been about to search criminal records by a Tax Id number? We've run a background check on just his name / birthdate (which was verified by his passport) and nothing is popping up in terms of criminal history. 

Thank you!