There are companies who will insure your lease payments, but you will have to provide them your SSN so they can run a credit check on you. Ultimately, it is up to you as the landlord to determine whether or not you want to require a Social Security number on your rental application.â–¡ Social Security number. The Rent Registry allows the City's Rent Stabilization Program to collect data on rent-stabilized apartments, monitor changes in tenancy and rents. The good news is that you do not need an SSN on an apartment rental application to screen a prospective tenant. Under California law, housing providers are not allowed in most cases to ask about or demand proof of tenants' immigration status. You have the right to ask for extra help with completing your application or with any other matter related to your CAPI case. Applicants must have an acceptable income and credit history.