Generally if something involves noticing something (aka it would have been a spot or listen check in 3.X) I've treated it as Wisdom (Perception), and if something involves investigating something in ways that involve physical manipulation or careful study it's been Intelligence (Investigation).

Lets see what 5.0 has to say about it:

5.0PHB177:

5.0PHB178:


We see a mild collision at first- is the broad synthesis of non-obviously related information a function of reason or intuition? "Both" is a satisfactory answer, but doesn't imply a solid mechanic for this.
But for investigating something, it's clear that the intended distinction here must be something about needing to reason it out. Lets go down to the subsection under each attribute and quote some of that:




So if you search a desk (or what happened in the session, an altar) for something that requires you to feel all around for it, try to hold a metal piece in one direction while pulling underneath a drawer, etc, I've been running that as investigation. I think I'll continue to do so, but you can see that this, like finding a trap, could easily be argued to be perception. You are literally trying to spot or detect the presence of something, after all.

A strong case can be made that the desk should have been a perception check to find the mechanism, and then an investigation check to figure out how to work it. I don't love that because it really makes it just a perception check (if the entire party fails the perception check it isn't found, but if a single one does, the item will get hammered out of the desk even if everyone fails investigation).

So I think I'm going to be a little bit arbitrary here- if careful study and reason is the better way to get to something, I think it's gonna be Intelligence, and if something is set up as a bit of a "puzzle" for your character to solve, then it's going to be Intelligence, and I think in almost every case that will be Intelligence (Investigation). But noticing something, including finding a trap, is going to be Wisdom (Perception), and that's going to continue to be the more commonly used skill.

As far as why I'm stretching Investigation a bit into a couple places Perception is arguably the more correct thing, it's because I think Perception is "too good" and I'd like if it wasn't the only applicable skill, and Wisdom the only applicable attribute, for these sorts of things. I like the idea of anything that arguably ropes in reasoning or connecting dots involving Intelligence. But I don't want to go too far here- the game has designed Perception as being "too good" for a long time and players definitely know that when building their characters, and I wouldn't want a Perception-stacked character to feel like they were being nerfed.



Thoughts?

Also when I went to hidden rolls for trapfinding rolls specifically, that's because a trap can be triggered on a low enough roll (if you're searching for traps without touching anything it won't trigger, but I'll roll with some trap-specific penalty plus disadvantage- this would also count as your trapfinding attempt ). If the rolls are out in the open, then the party will stop searching the moment a roll is convincing enough, and of course, you aren't supposed to know if your roll is good. Because that metagaming is effectively impossible to avoid without hidden rolls (everyone would have to predeclare a decision tree, lol), I switched to hidden rolls for trapfinding Wisdom (Perception) checks. Generally I'd like players to roll as many of their own rolls as possible, but searching for traps as I'm running it is an edge case I guess.