Hunt for the culprit. Every good story has at least one antagonist, but what steps must the hero or heroine take to find him/her? How will the villain evade the hero? How is the mystery solved? In mystery writing there are a lot of twists and turns. Write down your initial thoughts for plot twists, red herrings to throw the readers off the trail of the true villain, and of course the final stages of how the good guy will prevail...or does he? You need to decide whether or not the hero or the villain wins in the end. Many hero’s die trying to solve their case. Many are involved in physical altercations with other characters. You must decide how many altercations, the number of characters involved, and what weapons if any are used. It is not a good idea to only engage your characters with fist fighting. Throw in some knives, chains, falling from windows, or my favorite, a poisoning, and other nasty assaults.
For the Antagonist, decide the name, age, where does he/she live, is there an underlying reason for being the antagonist? Perhaps this person is a career criminal. On the other hand, maybe he/she is a good person that suffered an unjust and turned to crime out of bitterness and despair.
Then you have your support characters, who are the color of the story. They provide depth to the story whether good or bad. A support character could be as simple as a loud mouth hot dog vendor standing on a street corner or as in-depth as the villain's partner in crime. In writing a mystery story, support characters can take on a life of their own with the reader, so make them interesting. Just because they are labeled support characters does not mean they are any less important than the main characters.