Learn how to conduct fast, compliant background checks in NY in this comprehensive guide for employers and HR managers. How should I fill out an employment background check form if I have a criminal history?(The background check is post-offer.) All related (31). Based upon my experience an SSN is not required to run a background check. But it sure makes it easier. Click below for up-to-date forms and documents for use in submitting address or name changes, W4 forms for adjusting withholding status when needed. Applicants claiming these credentials will be required to provide proof as a part of the screening process. Work history information is used to determine whether you qualify for the job for which you are applying. It depends if you had omitted it on your job application. I believe the job application is what the background check will be based on.