According to Wikipedia, "For years, the film was not available in home video in any form. This was alleged to be due to music rights; reportedly, the distributors of Altman's films Images (1972), California Split (1974), 3 Women (1977), and HealtH (1980), had not negotiated music rights for home video release of the films, and, due to their relative obscurity, they were never expected to be released".
Robert Altman had a believer in the head of production at 20th Century Fox, Alan Ladd Jr.. He felt that he could indulge Altman's offbeat projects, while the studio's more commercial films like Star Wars: Episode IV - A New Hope (1977) would make up for any financial loss. Peter Biskind, author of "Easy Riders," reports in his book that Altman and Tommy Thompson were driving to the airport, when Altman said, "Let's stop at 20th. I had a dream last night, I want to sell it to Laddie. Keep the engine running, it'll only take a minute." Altman darted into Ladd's office, made a deal for "3 Women," and was back in the car in time to make his flight.
The movie opened and closed in a matter of weeks. As it had only cost $1.6 million, there was a minuscule profit for Robert Altman and Alan Ladd Jr., although the studio lost money on the distribution costs.
Shelley Duvall won the Best Actress Award for this film at the Cannes Film Festival in 1977. Duvall was also awarded the prize in the equivalent category from the Los Angeles Film Critics Association in the same year. Moreover, Sissy Spacek was awarded the Best Supporting Actress accolade for this film from the New York Film Critics Circle in 1977.
When Pinky spills the shrimp cocktail all over herself, originally filmed to scare Millie, she jokingly takes a knife and lays on the floor with it to make it appear as if she was stabbed. This scene was edited out but a segment was used in the dream sequence.
The trivia item below may give away important plot points.
Robert Altman says that the ending is meant to be ambiguous and open to interpretation. However, his personal opinion was that Edgar was buried under the pile of spare tires shown in the final shot of the film.