Doing a background check without a Social Security number from a rental can often be done. 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.A social security number is not mandatory for a credit check. You can order a credit report with a name and address. 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. This booklet explains many of these laws you need to know and provides resources where you can find more information about landlord and tenant issues. A typical background check only requires an individual's name and other information, while a credit check involves an SSN check. Personal and contact information. The good news is that you do not need an SSN on an apartment rental application to screen a prospective tenant. SSA shares this information with New York State, who will determine your eligibility for SSP benefits.