Well, Andy Williams' voice was recorded for the song "How Little We Know" by musical director Dudley Chambers, but his take wasn't used in the end. The problem with Lauren Bacall's voice was that she wasn't a professional singer by any stretch, and because her voice was so low and husky, it was extremely hard to find a female singer to dub her.
Piecing biographical bits together, the main issue was that the song contained two spoken lines, "Who can tell", and "As others have done", and as spoken by Bacall they simply didn't match Andy's singing voice. So it was decided to let Bacall do her own singing. If you listen to her recording on YouTube, you can tell it isn't Andy, because it's completely unlike his voice, and parts of it are off key or at least shaky.
Dicky