Peter did appear in other movies and his Columbo persona did follow him around. I recall the film Murder by Death (1976) and his acting is remarkably "Columbo-like". Perhaps it was one of these films you recall?
I think the poster might be thinking of an episode of "Streets Of San Francisco" where John Davidson plays a professional female impersonator who commits a series of murders.
I have checked this and I believe this is indeed the episode I refer to in my initial post.
It would appear that I cannot obtain a DVD applicable to Region 2 (Europe) but reading through the episode's write-ups and reviews I do identify with what is written. That there is a merging of the murderer's character (male/female) and that a murder is described as being committed by a classy dressed 'lady'.
Shall continue my efforts to obtain a DVD that I can view here in the UK.
Once again many thanks for your reply to my original posting.
There is an episode of Murder She Wrote from 1984, "Birds of a Feather" which features drag artistes.
Guest stars include Martin Landau (Mission: Impossible) as the murder victim, Jeff Conaway (Taxi), Gabe Kaplan (Welcome Back, Kotter) and Dick Gautier (Get Smart, When Things Were Rotten).
Jeff Conaway in drag is hideously ugly. Dick Gautier in drag is absolutely stunning. Angela Lansbury isn't in drag. Her character always dresses like that.
Thank you for your post and suggestion.
I am afraid it does not ring any bells so I think it is very unlikely to be what I viewed. Nonetheless worth having a look at the episode and the actors in drag.