For the most part the laws will be the same. It is still a contract between tenant and landlord...but like LAMAC66 said, your state or area could also have other requirements.
However, you will sometimes find exceptions. For example, if the property is a small owner-occupied multi-unit building (1-4 units), the landlord is allowed to turn down applicants with children. It is an exception to the fair housing rule for that one situation.