I'd assume it's Peter McConnell, the composer, as he tends to do a lot of the live instrumentation in his music; if not, it'll be somebody he brought in. Either way, it's very unlikely he released any kind of sheet music for it.
If you feel up to it you might want to try learning it by ear though; it's very satisfying, even if it it can take ages.
As a side note, if you love the Psychonauts music then you might want to check out the Grim Fandango soundtrack, which was written/performed by the same Peter McConnell responsible for the Psychonauts music (You can probably spot similarities in this
to a certain theatre!). Heck, the game itself was made by the same people responsible for Psychonauts so the best way to hear it would be to grab the game, although it's more focused on puzzles rather than action as it's an adventure game.