Good question - I was working along the lines of the murderer re-visting the crime in this head, which we get to see on screen...sometimes when Columbo first arrives at the murder scene and is questioning them..
Then, I thought no. Has it got something to do with the identification of the body by murderer or relative at the morgue....?
Perhaps not...when are you going to put us out of our misery?
Just one clarification. In A Friend in Deed it isn't the murderer (Halperin) who carries the body, but Hugh Caldwell. But I included it because my exact connection was "The body is picked up and moved to another location." I wasn't going to add in the fact that it was the murderer.
And as far as Etude is concerned, Jennifer Welles was not dead yet when Alex carries her to the kitchen.