Adding on to that... how exactly are you killing a character in Eclipse Phase? Is this perma-death or just their current Ego dies and the cortical stack is lost/destroyed. Is there backup available. Murder Mysteries are kinda hard to run in a setting where one of the basic premises is that Death is a minor inconvenience. The basic problem is well... why does anyone care? So someone's Morph died. Ohh well. And if its a perma death a larger question comes about in how? Because that means you hit every backup that person has, killed them before they could backup again, then destroyed their stack.

And as Acatalepsy pointed out, remember that characters have access to a lot of information in Eclipse Phase, quite a lot.

Honestly the main problem I see here is I'm not really sure Murder Mystery and Eclipse Phase go together particularly well...