IMDB has this credit for the song, crediting it to Carmen Lombardo, Edward Heyman and John Jacob Loeb, in 1937. From there the trail leads to the Canadian Songwriters' Hall of Fame CSHF , which gives you some history on the song. CSHF mentions that the song was used in the film "Dead End", also in 1937. The music credit for Dead End has some further detail, but without watching the film, I can't go further with that.
The fragment in the Columbo video seems to be a female vocal trio. Maybe this: the Mullen Sisters.
but given the age of the song, I can't be 100% sure - there could be many versions by female vocal trios, made since 1937, and that particular version may not exist on YT. The Mullen sisters' version is a complete version to listen to anyhow.
Various YT versions, found on the way, which are not the one, but maybe of interest if you like the song: 1937 version by Guy Lombardo and his Royal Canadians: male vocal trio. A version which mentions the use in the Columbo episode on an Italian album cover :