The purpose of the fair housing laws is to prevent discrimination on the basis of a person’s membership in a protected class. Nothing in the law forbids you from setting fair screening guidelines and applying them equally to all applicants.
Keep in mind that every person belongs to a protected class – each of us can be defined in terms of our race, color, religion, sex, handicap (disability), familial status, national origin, sexual orientation, source of income, age, or marital status. So any time you deny an applicant, you deny someone who belongs to a protected class. The question is whether or not you treat applicants (or tenants) adversely because of the class to which they belong. If the criteria you set are blind to class issues, and you apply them consistently, you may turn down applicants who do not measure up.
The key lies in making sure your process is fair – that it neither directly nor indirectly discriminates on the basis of one of the protected classes. To comply, you should design a fair process and apply it consistently and equally to all applicants.
You may have a rule that requires all applicants to show photo ID, and you could turn down applicants who cannot produce a photo ID. The practice becomes illegal if you apply the rule inconsistently – for example, requiring ID from people of one class but not from those of another.
You could give a document to all applicants that outlines rules of the unit and warns against selling drugs on the property. The practice becomes illegal if you hand the document to applicants of one class, but not of another. (Should you develop such a document, also make sure the language used does not discourage members of a protected class from applying.)
If someone provides you with false information or lies on the application, you may refuse to rent to them. This is both legal and highly appropriate.
There is nothing illegal about setting fair criteria and holding all applicants to the same standards. By the consistent use of such guidelines you can retain full and appropriate control over who lives in your rental units and who does not.
As you study the letter of the law, keep its spirit in mind as well. The sooner we remove the types of discrimination that weaken our communities, the sooner we can build a stronger, more equitable society.