Donna Douglas tested for a role.
Gore Vidal, who wrote the original play, was upset with the choice of Jerry Lewis as the lead in the movie version. On Broadway, Vidal's play ran for 388 performances between Feb 7, 1957 and Jan 11, 1958, and won Cyril Ritchard, originator of the Kreton character, a 1957 Tony Award nomination for Best Actor in Play. But Jerry Lewis was a star, twelve times named to the Top Ten list of Box Office Stars, six times with partner Dean Martin (with whom he was the top star of 1952), and six times solo (ranking as high as #3 in 1958). He got the part.
A poster for "Visit To A Small Planet" can be seen in "Breakfast at Tiffany's". It's on a wall in the final scene in the alley.
Prior to its successful Broadway run,"Visit To A Small Planet" was first aired as a television play on May 8, 1955 on the Goodyear Television Playhouse. While some sources places another broadcast of this play in 1957, Gore Vidal did publish a collection of television plays in 1956 entitled "Visit to a Small Planet and Other Television Plays". The play opened on Broadway on February 7, 1957 at the Boothe Theater and ran for 388 performances.