Crazy is written in the key of E Dorian.
According to the Theorytab database, it is the 2nd most popular key among Dorian keys and the 31st most popular among all keys. The E Dorian scale is similar to the E Minor scale except that its 6th note is a half step higher (C♯). Chord progressions in Dorian have a characteristic sound due to the major quality of the chord built on the 4th scale degree.
See the E Dorian Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!