"Murder By Suicide" is an actual script, written by an actual person (Frank D'Angeli), and it was actually purchased by the "Columbo" producers -- but it has never been produced, and it has nothing to do with "Columbo Likes The Nightlife".
Amusingly, over the years there have been reports of "Murder By Suicide" as an actual episode, starting as far as I can tell on the Internet Movie DataBase, and rumors spread from there to other internet "sources". The IMDb is a fantastic resource, but it takes anonymous information from anyone, and sometimes gets hoaxed.
I have even seen an ad offering "Murder By Suicide" on videotape or DVD. (One of the "Top 10 Signs Somebody Is Trying To Rip You Off": He's selling something that does not, and never did exist.)
This all came as a big surprise when I told Frank D'Angeli :^) about it.
So as a script, "Murder By Suicide" is real, and in theory might even be filmed someday. But as an episode, it's a myth -- like such other rumors and hoaxes as "Columbo: The Juggler" and "Columbo: The Man Who Murdered Himself".
Incidentally, Frank wrote a nice piece in the Scrapbook area of this site ("An Open Letter of Thanks"), although he modestly gives way too much credit to this web site in the eventual sale of his script. Frank also ghost-wrote the Scrapbook article "Our Day At The View", and was one of the special guests invited there by yrs truly.
Well, Bob, the IMDb itself, everybody's favorite source, now claims that "Muder By Suicide" was the "working title" of "Columbo Likes The Nightlife", so you are in good company.