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. Doing a background check without a Social Security number from a rental can often be done.A social security number is not mandatory for a credit check. You can order a credit report with a name and address. The good news is that you do not need an SSN on an apartment rental application to screen a prospective tenant. A typical background check only requires an individual's name and other information, while a credit check involves an SSN check.