Doing a background check without a Social Security number from a rental can often be done. The good news is that you do not need an SSN on an apartment rental application to screen a prospective tenant.I was told I needed to fill out a rental application (where ssn is required) before viewing it because he gets several requests a day. â–ˇ Social Security number. You should be able to rent an apartment without a Social Security number provided you have a student visa or Permanent Resident Card (a.k.a. Since the SSN is a required field, have them temporarily enter any 9-digit number so they can continue filling out their rental application and complete it. However, a landlord can and should ask for a ITIN number when screening a potential tenant, if a tenant doesn't have a social security number. If the applicant does not have a social security number, you generally can't run a credit report or nationwide criminal check. It is not usually necessary to request a Social Security number (SSN) on an MI rental application. However, a landlord can and should ask for a ITIN number when screening a potential tenant, if a tenant doesn't have a social security number.