Well, you could always assign a skill literally called Investigation for a LE type character, or Logic to cover both deduction and induction. Some Traveller versions after CT have Investigation I believe.
Intelligence is obviously the ruling stat for this, in my case since my IMTU task rolls are stat+skill based +/- difficulty it looms rather larger then most system rolls.
Education however should be a big part of the deductive process and therefore roll(s). Having background knowledge that applies allows more rapid pattern recognition and previously noted modus operandis and/or professional knowledge about how specific people will act within their training.
A knowledge check for personally known background should include the education stat, and applying skills when appropriate (so Tactics for violent crime scene forensics, Administration for tracing embezzlement or fraud, Computers for hacking moves, Legal for figuring out what evidence or witnesses are critical for prosecution and thus targets, etc.).
Jack of all Trades can be a decisive skill here, and would handle superdetective/psychology rolls for Holmes and Reacher types.
Other more mundane/mortal people would consult experts on a given evidence/psych behavior/training issue, the extant Interrogation skill could be used by the deductive character to question experts and possibly gain a temporary + mod for specific knowledge applied to the current problem.
I also use a home rule of converting 1 Education stat into 4 knowledge specialties in whatever combination. I use this so people can have interesting hobbies or expertise not covered in base skills, so sometimes those can come into play, or this mechanism covers a consulted experts' knowledge. Other post-CT systems are apparently working this direction as well.
I usually have knowledge success modify difficulty level of the actual deductive intelligence roll- other systems require X amount of success checks for a particular investigation. Your solution may vary.
Final thought, you will need to have material prepared if your players develop a taste for or you make known that this sort of action is possible in your sessions, or at least know your NPCs well enough to make snap judgements about what they will do and why.