Groovy. I love murder mystery stories but they're hard to do in the Trek universe because the technology often trumps so much of the 'old fashioned' detective work. I think your technique of using red tape to place constraints on the characters should be very effective. Things like DNA, security cameras, and witnesses can help keep the ball bouncing but the trick is finding ways so that they only feed part of the story each. Another good trick is if the murderer uses technology themselves to mask their guilt. It's intriguing so far
I am going to do a sort of murder mystery for my next Trek story too, albeit that's only a small part of my overall plot.