This actually a number of questions that conform to the title question, and which all stem from a bit of rules confusion.
Let's start with the rules confusion.
On pg 178, under the skill Investigation the rules says the following;
You might deduce the location of a hidden object,…
On the same page, directly to the right of the investigation skill, is a green box titled Finding a hidden object. In the box the rules says the following;
When your character searches for an hidden object such as a secret door or trap, the DM typically ask you to make a Wisdom (Perception) check.
Now here we have two skills that clearly does the same thing.
So my first question is: Are the skills interchangeable or mutually exclusive?
That is: can you use either skill to search for traps in any situation, or do you use Investigation only in specific situations you can't use Perception in, and Perception only in specific situations you can't use Investigation in?
My second question is: What do you use to make passive checks to spot a trap?
Do you only use Perception, as you would if a character did not have proficiency in either skill?
Or, if a character is proficient in Investigation but not Perception, would you then use Investigation instead?
Which leads me to my last question: What if a character is alert to the possibility of hidden objects like traps, but isn't actively searching for them?
In other words, what happens if a player utters the oh so familiar words: "I'm prepared for the possibility that there might be traps in here."
He/she isn't actively searching, but it isn't exactly passive either. If the character has proficiency in Investigation, do you then use that skill, or do you stay with Perception checks?
In other words: when do you use what skill?
Best Answer
Perception is for observation, Investigation is for deduction.
Some of this answer will be observations on how Wizards has done it so far and some of this will be logic, and some of it will be mechanics.
First for the headline question. It depends. when to use Investigation, and when to use Perception is not entirely clear yet, and I'm hoping we'll get more guidance in the DMG late this year. The guidance from the rules is that the two skills mostly seem to differ in the methods by which they are found.
Depending on the exercise, either, or both of the skills may be used.
For passive checks, you're almost always looking at Perception being the skill of record. While all skills can be used passively, some skills make more sense than others. Perception is the hallmark passive skill, whereas investigation makes less sense as a passive skill.
If the character is alert to the possibility of hidden objects/traps, but not actively searching, he's using passive perception.
The guidance for this seems to be (though we can't confirm yet), that the DC for actively looking for something is regularly about 5 less than the DC for passively looking for something (or sometimes actively looking always reveals it).
So here's how I would play it. Traps can be noticed with perception passively (usually DC 15). If the PC is looking, ask them how they are looking. If it's observational, then use Perception. If it's deductive, use Investigation. When they are searching for items, again, either skill is appropriate. This is somewhat counter to how WOTC has written adventures so far. They are always written to use perception to notice traps. Passive with a higher DC and active with a lower.
Investigation also has broader uses such as when you are trying to track clues, or put something together. It's also a great "roll for a hint" kind of skill if your PCs get stuck and need some help figuring out what to do next.