Be careful with this. The Fair housing act is kind of open here.
While the above concerns are legitimate, there are some popular but unfounded generalizations about undocumented persons that a landlord can safely exclude from his or her rental decisions. For example, the claim that undocumented immigrants are associated with increased violent crimes has been debunked by nonpartisan studies, as has the claim that undocumented immigration is associated with increased drug crimes.
A landlord who makes rental decisions based on such generalizations could run afoul of federal and state housing laws. Both the federal Fair Housing Act ("FHA") and the Pennsylvania Human Relations Act prohibit discrimination in housing based on race, color, national origin, religion, sex, familial status, and disability. Although the FHA does not specifically prohibit discrimination based on "citizenship status" or "immigration status," denying housing to undocumented persons could constitute discrimination based on "national origin" where the discrimination is based on the tenant's language or national origin in general, regardless of immigration status. The Department of Housing and Urban Development has clarified that undocumented persons do have the protection of the FHA where they are denied housing based on any of the listed classes. Similarly, the Pennsylvania Human Relations Act could be applicable where a landlord rejects an undocumented person as tenant based on their ethnicity or national origin rather than simply their immigration status.
So just make sure you protect yourself and keep your practices the same. If you require a background check and you cant do one on someone then that is in line with your requirements. I am not a lawyer and you should check with one because what I said is my educated opinion and nothing more