The Fair Housing Act gives people protection against being discriminated against for reasons relating to being part of a particular group. The protected classes that fall under this act include race, color, national origin, religion, sex, familial status, and disability. Your screening criteria may have an unintentional bias against one of these groups.
Some of the most common areas that landlords trip up on when it comes to fair housing laws is putting different standards in place for different types of renters. For example, you can't have a different set of requirements for a family as you would for a single person for an application approval. The required income levels and credit scores should be the same for each applicant.
Discriminating against someone’s family status is different from denying them if the occupants would exceed the legally allowed number per size of your home (measured by bedroom amount). Discrimination in this area would be if you denied a family of four because they have three young children, but approved a group of four adults.
You also don’t want to put any language in your rental listing that indicates a preference for a particular group. By placing a preference in your advertising, you are discriminating against the protected classes that you don’t include.
It’s possible that your state has additional protected classes, such as sexual orientation, that you would need to keep in mind when you’re screening tenants.