Since 'Chungking Express' was filmed in sequence or "like a road movie" as Kar-Wai Wong has said, Wong wrote each scene either the night before or in the morning of the day of filming.
The filmmakers were sued by the people living below the apartment that was flooded for one scene. The apartment was on the third floor and both levels below it suffered water damage.
Faye Wong is better known in Hong Kong as a pop singer. Indeed, that is her singing on the cover version of The Cranberries song "Dreams" that we hear during the film.
A third segment was written but Kar-Wai Wong felt that the film was complete without it. The third story formed the basis of Fallen Angels (1995).
Quentin Tarantino signed a deal with Miramax specially to start his own releasing company so that he could get Chungking Express (1994) out to a wider public.