Columbo whistling or humming this tune is one of those idiosyncrasies that we got used to over the years. I always thought that it was something that they introduced in one of the later seasons. Does anyone know which episode we hear it for the first time?
For some reason I thought I first heard it in A Stitch In Crime when Columbo shows up in the garage with his boiled egg but maybe I just wasn't paying enough attention in prior episodes. Probably the first time he shows up with an egg too. That was a short lived thing.
He first whistled it in Any Old Port, he was doing a scene on the phone and while he was on hold he started whistling it, it was an ad lib moment that he made up during the scene.