I am watching again all Columbo episodes from the beggining (exciting stuff :D). And I asked that question here couple of times but I never got a clear answer. What is this Tommy scene about? was he in cahoots with dr Flemming? why did he confess? what was the point of it all? it is never explained...
not sure other than he could have been a set-up just so Columbo could see Flemmings reaction. Also there was the bit, "he's lying, he didn't do it" I'm sure Columbo already knew that. It also could have just been a "twist" like a lot of mystery shows from 1968 did.
As far as I understand, he's one of those people who go around confessing to things they didn't do, and he gives off that kind of vibe, so Flemming (being a psychiatrist) has to say so.
Of course, he does halfway accuse Columbo of setting up the whole thing, so I'm not sure.