Landlords can legally ask for social security numbers on rental applications as long as they are not doing so in a discriminatory manner. Doing a background check without a Social Security number from a rental can often be done.Ways to get a background screening without a social security number for renters and buyers, we look at credit reports, criminal and civil records. The good news is that you do not need an SSN on an apartment rental application to screen a prospective tenant. Without a valid SSN or ITIN, you may not be able to verify credit history, income history, etc, so you may be taking on additional risk. If you apply to rent a place to live, the landlord may "screen" you. Some landlords will also ask for your social security number or government ID information. There is no Need for a copy of your social security card. Religion is also on the don'task list. â–¡ Social Security number.