Melodramatic comedy requires characters to be larger than life, and more than a little flamboyant. Your average person is not a murderer -- it takes a special breed. Trapeze artists, clowns, lion tamers, Senators, bimbos, reporters, hobos, Nazi spies, fading film stars, temperance crusaders, communist operatives, Mafiosos, archeologists, heiresses, inventors, you name it -- all have been suggested by unusual environments in past On The Edge mystery shows.
The hardest kind of character to write for is the Average Joe, the normal guy with no outstanding characteristics. The more outrageous the character type you can come up with, the more they will almost write themselves.
If you know the strengths and weaknesses of the cast that will perform your work, you can use them as a basis for the character. If one of your actors has a particular skill, work it in -- the character of Spunky the Clown in my show The Dying Old Man on the Flying Trapeze was written for actor Allen Klesh, an accomplished magician and juggler, so, Spunky juggled and did magic tricks. But don't let current capabilities become a straightjacket, your cast should be willing to stretch. When Klesh left the cast and Pat O'Connell took over the role, O'Connell had to learn how to
A certain amount of stereotyping can be useful, not in a hateful, racially or gender biased way, but in terms of the kind of stock characters we are all used to from the movies and television. You can use these familiar character types. The dishonest congressman, slimy political boss, iron-willed politician's wife, etc., are instantly recognizable and allow you to get on with the plot with a minimum of character development, or to play against type for humor or surprise, as with a creating a weak-willed strongman.
Keeping your characters clear-cut types possessing only a few strong emotional
traits may not make your play realistic, but it will help the audience keep who's who straight, and assist them in solving the mystery.
A mystery, of course, requires a victim -- preferably a character that isn't too sympathetic, so that his murder will seem a just desert rather than a clear tragedy. You must create a victim that everyone in your cast would be happy to see dead, so that they all will be suspect.