This is a form of theatre sometimes done as dinner theatre. It involves some kind of who-dunnit and is meant to be light entertainment. There are companies like Eddie May Murder Mystery Dinner Theatre that buy scripts or buy and revise scripts to fit this format. This is a kind of theatre written to be performed in a particular environment, perhaps on a boat or traveling train. There is a kind of theatre now that, say, stages a wedding, and actors and audience intermingle.
Musicals There are production companies that specialize in producing musicals.
Play Publishers Play publishers like Samuel French publish plays and offer their production rights to theatres. Getting published used to mean that a play was produced and reviewed in New York. That doesn't have to be the case now, particularly for plays written for schools, churches and community theatres. Most play publishers will send guidelines about what they expect in terms of submissions. Meriwether Publishing Ltd. PO BOX 7710, Colorado Springs, CO 80933.