I always imagined it as starting out as a Columbo mystery where the audience knows who done it and Mrs. Fletcher is in town to promote one of her books and gets wind of the murder and accompany's Columbo along as he brilliantly lulls the suspect into a false sense of security.

Even Jessica Fletcher would believe Columbo to be absent minded until the time comes for him to confront the murderer then she sees how its all an act to get the suspect to let their guard down.

The way they meet is the first time Columbo has her sign a copy of her book for his wife since she is a big fan of J.B. Fletcher and then later when Fletcher is snooping around the crime scene she runs into Columbo again and only then finds out hes a police Lieutenant and they work together to solve the crime.

Sounds like a good idea.

There was an Alias/Columbo crossover spoof.

Yes, the Alias and Columbo spoof was excellent. A remnder, fr thise who haven't seen it for a while:

https://www.youtube.com/watch?v=nSyeQH15evw

or the other possibilities from the Sunday night mystery movie rotation they had in the 70's which included 'Macmillan and Wife' and 'McCloud'.

I've said it a dozen times, but I've always suspected that "A Friend In Deed" was a kind of MACMILLAN AND WIFE joke. In a small way, I mean. If so, a joke like that is sort of the next best thing to a crossover.

Uneasy Lies The Crown was a rewritten McMillan episode, in which Nancy Walker from McMillan appears as herself who acted in McMillan!