Does Lt. Columbo have an imaginary wife?

There is a whole page devoted to answering this question on one of the fan sites.

It lists at least three characters who say they have seen/interacted with Mrs. Columbo.

1. In Troubled Waters, the ship's captain assures Columbo that he saw Mrs. Columbo get on board.
2. In Caution: Murder Can Be Hazardous To Your Health, the dog groomer got instructions directly from Mrs. Columbo.
3. In No Time To Die, Columbo is at the wedding of a close family member, and is asked about his wife.

None of these are really concrete evidence she exists, but I think together they should be sufficient enough to say Mrs. Columbo is in fact a real person. Also, in several episodes, Columbo is seen talking to his wife on the phone.

His speciality was manipulating people. Therefore she was nothing more than a device for the purpose of breaking down barriers of those he was interrogating. I've never seen his wife in any episode. Nor has anyone else. "Oh, and just one more thing." She was under the weather, and unable to accompany him at verious engagements frequently. I think perhaps he was referring to his dog, who oddly enough was in several episodes. Case closed!

"His speciality was manipulating people. Therefore she was nothing more than a device for the purpose of breaking down barriers of those he was interrogating."

Yes, this is how I always took it and I loved it since it perfectly fitted Columbo's cunning character. I was therefore rather annoyed when in the later episodes (mentioned by another post above) he did actions which contradicted it. It in a way imho damaged who Columbo is. Making "fake wife" to his suspects was imho just another brilliant way how to lower their caution.

I try to pretend those episodes which make her "real" even if still hidden did not happen. :-P

But strictly speaking - there is (unfortunately) now quite a clear evidence she is a real person. He could in theory fake phone calls despite being alone and thus having no one to fool (but I'd really hate that since it would mean he is a bit schizophrenic and crazy, what Columbo imho surely isn't), but in few episodes other people talk about her (ship captain for example) what would make no sense if she wouldn't existed.

Yes she does exist, she even had her own spinoff:

From Wikipedia:

Shortly after the Columbo series ended its original run on NBC in 1978, despite objections from Columbo producers Richard Levinson and William Link, NBC executive Fred Silverman went forward in producing Mrs. Columbo as a spin-off to the original series. The information NBC released about the show was unambiguous about the fact that Mrs. Columbo in the new series was in fact the previously unseen wife frequently mentioned on Columbo.

The show received poor ratings, however, and as part of efforts to revamp it, the linkage between this Kate Columbo and the Mrs. Columbo of the original television series was reduced. The name of the character was changed to Kate Callahan after an off-screen divorce, and the series was renamed Kate the Detective, followed by Kate Loves a Mystery.

https://en.wikipedia.org/wiki/Mrs._Columbo

It starred no less than Captain Janeaway herself, Kate Mullgrew

As previously written, he does phone her beyond or out of cases so it would be odd if she was fictious (made up by Columbo himself). I believe they tried to give her her own TV series, but surprise surprise it did not work and it got canned.