Though the movie is set in Beverly Hills, the majority of the movie was filmed in Mexico. Rodeo Drive was reconstructed out of Styrofoam in a lot outside of Mexico City.
Orion Pictures was originally set to release the film in the summer of 1991 but they fell into bankruptcy before the film could see the light of day. Columbia Pictures eventually picked the picture up and gave it a small, and brief, run in the fall of 1991.
Harley Jane Kozak was chosen for her role after being passed over for a role on Wiseguy. One of the producers worked on both productions, and really liked her. The only caveat was that she impress Ken Wahl, which she did.
Ed Kelvin: [Conluding his opening monologue on Beverly Hills]
... Of course if you're a beverly hills cop like me you just can't afford to live here... makes you think doesn't it?