Usually, yes - an active search effort is required.
The rules seem to presume that characters do not notice traps unless they are actively looking for them, though some characters may have abilities which change this rule. For instance, the text of the Find Traps spell states:
You receive a check to notice traps within 10 feet of you, even if you are not actively searching for them.
This implies that if you are not actively searching, you do not get an automatic check to notice a trap. The Rogue Talent Trap Spotter is similar:
Whenever a rogue with this talent comes within 10 feet of a trap, she receives an immediate Perception skill check to notice the trap. This check should be made in secret by the GM.
And the Dwarven racial feature Stonecunning grants the same thing to all dwarves in relation to unusual stonework:
Dwarves gain a +2 bonus on Perception checks to notice unusual stonework, such as traps and hidden doors located in stone walls or floors. They receive a check to notice such features whenever they pass within 10 feet of them, whether or not they are actively looking.
None of these abilities would be worth much if you could already always make a reactive perception check to spot a trap.
However, a GM might sometimes rule that a trap is obvious enough that anyone can make a reactive perception check to spot it; some traps just are not particularly hidden. You could imagine, for instance, a swinging spiked log that is just attached to the ceiling of a corridor; the characters might not notice it, because it's dark and they'd have to look up to the ceiling, but it is not really so hidden that it requires active searching effort to be able to spot.