i did a bit of research & Lauren Bacall did indeed do her own singing in TO HAVE AND HAVE NOT:
"When it was decided that Bacall's character would sing, the studio and Howard Hawks ordered some vocal training with Warner vocal coach Dudley Chambers. In case she wasn't up to the challenge, several singers were called in to audition for the dubbing, among them torch singer Lillian Randolph and Dolores Hope (wife of Bob). Louanne Hogan, who was at Warners at the time assisting Joan Leslie with her vocals in Cinderella Jones, was in on the fun as well. "Yes, I auditioned for the dubbing of Betty Bacall in To Have and Have Not," Louanne told me recently. "I tried out, but my voice just didn't fit her at all. It fit Joan Leslie just fine. If I'm not mistaken, Andy Williams got the job." The then teen-aged Williams did win the auditions and recorded the numbers.
Bacall evidently unsuccessfully recorded the numbers. Says Tod McCarthy in "Howard Hawks: The Grey Fox of Hollywood": "Williams finally prevailed, and it was his voice that emanated from the playback machine ... when Hawks at last came to filming 'How Little We Know.' As was customary, Bacall sang along while [Hoagy] Carmichael tinkered away on the silent keyboard, and as she did, Hawks liked what he heard and told her to keep going. When she was done, he decided to record her again singing the song, so, despite the legend that has come down over the years that Andy Williams' voice was dubbed over Bacall's, the truth is that Bacall sang her own numbers in To Have and Have Not." Andy Williams wasn't left in a lurch, he appeared in a few bit roles at WB, such as Janie (1944) and The Big Sleep (1946).
The two songs Bacall was required to sing were the newly written "How Little We Know" by Carmichael and Johnny Mercer and "Am I Blue?" The latter song was penned by Grant Clarke and Harry Akst for the earlier Warner Bros. film On With The Show (1929), where it was sung by Ethel Waters. Warners obviously thought highly of the song. It was also featured in their So Long Letty (1930)."