In which film does the hair-tossing Rita Hayworth sing "Put the Blame on Mame"?

The 1946 film, where the hair-tossing Rita Hayworth sings "Put the Blame on Mame", is "Gilda". "Gilda" is a film noir directed by Charles Vidor. It stars Rita Hayworth in her signature role as the ultimate femme fatale and Glenn Ford as a young thug. The film is known for cinematographer Rudolph Maté's lush photography, costume designer Jean Louis's wardrobe for Hayworth (particularly for the dance numbers), and choreographer Jack Cole's staging of 'Put the Blame on Mame' and 'Amado Mio', sung by Anita Ellis.

Johnny Farrell (Glenn Ford) is a small-time American gambler, newly arrived in Buenos Aires, Argentina. When he is caught cheating at a game of blackjack, Farrell manages to talk his way into a job with the casino's owner, the powerful Ballin Mundson (George Macready). The two form an uneasy partnership based off their mutual lack of scruples until Mundson introduces Farrell to his beautiful new wife, Gilda (Rita Hayworth), who just happens to be Farrell's ex-lover.

"Gilda" is a film which was produced by Virginia Van Upp. The screenplay was written by Jo Eisinger, Marion Parsonnet, and Ben Hecht (uncredited). Distribution was provided by Columbia Pictures in April 1946. It became a critical and commercial success. In 2013, the film was selected for preservation in the US National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant".