What is a good investigative RP game?

[Karnitis]

I have a friend who wants to DM a game which he describes as 'murder mystery on a spaceship.' We have played 5e DnD & Call of Cthulu, and while he likes D&D moreso, he vastly prefers the CoC skill system. To which, I agree. While 5e does give you over a dozen skills to specialize in, you get three times as much in CoC. Additionally, rolling a percentile dice is more appealing to him over a d20.

He says he may go with CoC, but without the insanity points or anything like that, since this will be more roleplay than combat. But do yall have any suggestions for an RP system that has the best/most diverse skill system?

[Grod_The_Giant]

The GUMSHOE engine is built around exactly this sort of game. Trail of Cthulu is probably the biggest name, but Ashen Stars (looks like the idea is "if Raymond Chandler wrote Firefly") might be right up your ally.

Speaking of Stars, STaRS works pretty well for this sort of game. Not on the "granular skill list" side of things (it's pretty much the opposite-- ability checks only), though you could easily hack something in, but the social and environmental conflict engines are robust enough to handle a non combat-focused game. The latter in particular can be used as a framework for all sorts of investigate-y things, like hunting for clues or trying to track down a rumor. If you're interested (or maybe even if not, ideas are percolating), I can toss together a set of Mystery expanded rules.

[Tinkerer]

You can also just homebrew a more in depth skill system super easily. Like, it's literally just a list. Unless the skill system is tied in heavily to other mechanics (like abilities) I often do this just to give my campaigns a little extra flavour. Just remember that having more skills doesn't increase the number of options the players have, it decreases them. The more precise the skills are the more you're saying to your players "You can't do this action unless you have this particular skill".