To show a movie to a group, you need to purchase a public performance license. Unless you purchase a license to show the film, you would be showing the movie illegally by breaking copyright and public performance rights laws. Please see the Public Performance Rights page for more info.
Public performance licensing of movies isn't as clear as we would like it to be. There are currently no industry standards for how and where to license every movie, making it a challenge for people who are trying to do the right thing and support Christian film.
Film licenses are determined by the producer/distributor. Sometimes they offer licenses through CVLI. (See the CVLI Producer list here: http://cvli.com/producers/family-values-package/ )
Sometimes the producer will license it directly themselves through their own website. Sometimes they allow websites like ours to sell the license on their behalf. We are working on adding more like this everyday to make it easier for our customers as this is a common request.
Other outlets that license films for churches: http://outreachfilms.com, http://lifeway.com/films, http://www.providentfilms.org/movieevents
We sell the DVDs for all of these films, but not always the license. The movies we can sell you a license for are shown here: http://www.christiancinema.com/catalog/default.php?cPath=180_127_256
When in doubt however, unfortunately, you have to find out on a movie by movie basis from the producer/distributor how they decided to offer public performance licenses.