Here are two video excerpts from that episode the provide a great showcase for Cooper. But a word of warning - if you haven't seen the episode yet, that second video is the solution to the murder!
From the best damned 'Columbo' website online:
Columbo alludes to Candidate For Crime in both of the episodes that immediately followed it in the original broadcast schedule.
In Double Exposure, Columbo says that he has been "working late on the Hayward case." There can be little doubt that Columbo means Nelson Hayward, the politician who murders his campaign manager in "Candidate For Crime," because "Double Exposure" was the next episode after "Candidate For Crime". This is an unusual acknowledgement that Columbo must handle multiple cases at the same time.
Then in the next episode, Publish Or Perish, Columbo tells killer Riley Greenleaf (Jack Cassidy) that he wants to write a book about his experiences as a policeman. As an example of his potential book material, Columbo describes the plot of "Candidate For Crime". Greenleaf responds, "Lieutenant, very frankly, I don't give a damn about your Senator or your story."