The release of the "So Crazy / Come" single was first reported by news media outlets on September 4, 2003. Initial reports of the single indicated that it would include three original songs, however, the released single only came with two. A promotional photo used in news reports pertaining to the single depicted Amuro with one foot on top of the letter "A".
Snippets of the music video for "So Crazy" were premiered on the daily early morning news program, Mezamashi TV on October 3, 2003. The full clip would debut two days later on MTVJapan. Directed by Musashi Muto, "So Crazy" takes place in an empty parking lot. Similar to some of her most recent videos, this clip focused on dancing rather than crafting a story around the song. Extras were used as background dancers to create a sort of clubatmosphere. Parts of the video were also filmed in green screen to include a double of Amuro. The second Amuro, dressed in a leather jacket and miniskirt, appeared in the background dancing with the extras. Both images of Amuro appeared together as one would sing the verses and chorus while the other would sing the ad libs. The clip emphasized this by zooming in on whichever image of Amuro was singing and blurring the one that was not.
A music video for the other a-side, "Come," was never produced.