It is my personal opinion that psycological thrillers should be done in first person, through the eyes of the crazy spooky person! But that might just be me!
First person definitely makes it easier to explore the psychology naturally. But it might be spookier to do it in the first person who is around the spooky person, that way they don't fully understand, they just see the effects.
I find that Ted Dekker is a stupendous thriller author, and I've never once seen him use first person perspectives except for his characters' thoughts. And he only occasionally switches to the perspective of the villain, if only for a tiny bit of insight. Maybe I'm a bit biased in favor of third person, or maybe I just haven't read enough of the genre, but I think Dekker's style is as close to perfect as I've ever seen.
What if there is no crazy spooky person in the story...? I might have a flawed understanding of "psychological thriller"; maybe I'm thinking in terms of "psychological suspense." But either way, I didn't think there had to be a crazy bad guy or anything; I just thought the fear in the story had a strongly psychological, as opposed to slasher/gore/supernatural or something, angle. Sometimes our greatest fears are ourselves. (At least, that's the premise I use a lot in my own psychological-themed writing.) First person might work for some such stories but it seems like for others, it might give too much away or take away from the suspense if the reader knows who the bad guy (if there is one) is or what his/her motives are (from being in his/her mind all the time). It'd be interesting to peek in on their thoughts if they're truly nuts, but that might be hard to write convincingly without sounding trite. Like, "The voices, the voices tell me to do it!" *rolling eyes*
The perspective of the "crazy spooky person" should indeed be the focus, but don't confuse that with first person sentence form. You can write from the perspective of Mr. OddLoner in third person, dipping occasionally into his inner dialogue (which would be in first person), and narrated from his perspective (which describes the world around him in character-driven narrative, mostly in third person).
I find that John Katzenbach's "The Madman's Tale" does this nicely (The books is basically the MC telling a story, but there are also some parts [in third person] which describe the present). FMK: Nice avatar .
