Was it claymation?
There may have been some claymation in it I just remember the guy in the trench coat suit and hat talk/singing food words to tell a mystery in film noir style black and white - so there would be a line like ‘celery wanted me to take the case’. Instead of she really... But I remember the talk/sing being set to music and was written much better than anything I could come up with ... I’ve been trying for nearly 20 years to figure it out. Funny as could be and makes you want to set through to see what other use for the words the could come up with...