Did Rita Hayworth do her own singing?

That's a myth and it's, sadly, not true. It started when Gene Ringgold wrote in his book "The Films of Rita Hayworth" (1974) that Rita supposedly sang the acoustic version of "Put the Blame on Mame" herself, but he didn't mention where he had gotten this information from.

At the San Francisco Film Festival in October 1972, Rita did say that she sang this version of the song herself. (There used to be an audio file of her interview online, but I can't find it anymore.) However, during the interview, she sounded very tipsy and she also suffered from Alzheimer's pretty heavily at the time already, which doesn't make Rita a reliable source in this regard. I assume that Ringgold knew about this interview and used this new information for his book two years later.

Columbia, on the other hand, denies, ever since the old studio system broke down and until this day, that Rita ever sang herself on film. If she had actually sung this version herself, why does Columbia not use it to market dvds of "Gilda" and Rita's box sets or whatever? It would make the film even more interesting to film buffs and collectors. Why would they deny it? They should have all the information on the production of "Gilda" in an archive after all. So they should know.

Also, if you listen to the two different versions, the nightclub and the acoustic version, you can still tell - despite the different tempo and the different instruments - it's the same voice and singing technique, that of Anita Ellis.

Nightclub version:
https://www.youtube.com/watch?v=e-LO9Ay6v_M

Acoustic version:
https://www.youtube.com/watch?v=v3uzB-q0jsU

The song "Please Don't Kiss Me" in "The Lady from Shanghai," where Rita was dubbed by Anita Ellis once again, is also very telling. It is as slow and as atmospheric as the acoustic version of "Put the Blame on Mame" and the voice sounds just the same. And there has never been any mention that Rita sang "Please Don't Kiss Me" herself, too.

"Please Don't Kiss Me"
https://www.youtube.com/watch?v=Q3j6sWAJ45Y

And why would they even have to dub her if she could sing like in the acoustic version of "Put the Blame on Mame" and "Please Don't Kiss Me"? The two songs sound just perfect.

Rita sang herself on tv shows in the 70s, though, like on the Merv Griffin Show, and her voice and singing technique sound pretty different (the similarity to her speaking voice is very evident, though, unlike the singing in her films).

Rita singing with Merv Griffin:
https://www.youtube.com/watch?v=GNJwLys_aHU