Oddly enough, Griffin only chose one song that Ginger recorded for film.
The first song was "They Can't Take That Away From Me" from the Gershwin score to "Shall We Dance":
but it was a song that Fred Astaire sang to Ginger's character:
The second song was "But Not For Me" from the Broadway show "Girl Crazy", in which Ginger played the lead on stage
Rogers is depicted second from left in a rather unflattering Hirschfeld cartoon of the cast:
A clip from the documentary "Astaire and Rogers: Partners in Rhythm"
Ginger Rogers wrote in her memoirs that her castmates accidentally used her real name on stage in the middle of a performance. Since the audience thought it was funny, they kept it as a bit. She contended this was the reason MGM changed the name of the character she played from Molly Gray in the stage production
to Ginger Gray in the film:
Rogers' character was depicted on screen by Judy Garland.
The third song was "The Continental" from Cole Porter's "Gay Divorcee"
I only remembered the dance finale in which Ginger didn't sing:
but she did sing the lyrics to the song earlier in the film:
The final song was another selection from "Girl Crazy," "Embraceable You"
Again, sung by Judy Garland for the film adaptation:
Ginger recorded a slow dance jazzy disco version in 1978: