Any public screening of a copyrighted work requires proper licensing - even for a nonprofit or educational entity. Renting or owning a copy of the film does not carry the right to publicly screen the film (though private viewing by family or a few friends is okay). In order to adhere to copyright law you must purchase public performance rights or a public performance license. Willfully infringing the Federal Copyright Act (Title 17 of the US Code) is a crime.
The Enoch Pratt Free Library has a very helpful resource for learning more about screening films, including a list of vendors that sell Public Performance Licenses: How Do I Find Out if a Movie Has Public Performance Rights?
Films in the public domain are exempted from this law and may be screened without license or permission.