Sorry, that didn't happen. Columbo did come across Little Richard once, but I doubt you'd confuse Alice and, er, Little.
More likely you're thinking of the Monk episode which indeed featured Alice Cooper. Monk, knocked way off his game by the mounting stench from a garbage strike, becomes convinced that the murderer was Alice Cooper.
I don't think I would mistake Monk for Columbo, but the episode I was thinking about must have been thirty-five years ago, maybe longer ago that that, and I must admit my mind isn't the same now as it was then.
He also has a Cameo in the Johnny Depp movie Dark Shadows. He plays himself. One more thing about ALice Cooper. He came out of the closet and revealed that he is a Christian!!!
I've done this too--I've been absolutely convinced that I saw a certain scene in a Columbo episode, only to confirm (after getting all the episodes on DVD) that it simply never happened. I assume that I saw the scene on some other show and just got confused, even though I have oddly specific memories of the lines coming out of Columbo's mouth.
John, thanks for speaking up -- it's a common trick that the mind plays on us, no need to be embarrassed, and yet some fans will go to great lengths to INSIST they saw a "Columbo" with George Kennedy, or one where we meet Columbo's brother from out-of-town, etc. It happens to the best of us, and probably more often to the best fans.