I amazed anyone can have avoided seeing Columbo Ron!n, it's been around twice as long as you have !
He was as shambolically disgustingly untidy, as Monk is neat. It was a groundbreaking show though, in that, unlike every other detective series, it was not a whodunit. You saw the murderer commit the perfect crime at the beginning, but Columbo would see through the alibi and spend the rest of the time badgering and eventually trapping the killer.
To that extent I will concede some similarity with Monk, who frequently is in the "I know you did it, and I'm going to prove it" genre, but not exclusively like Columbo (that was the unvarying format for decades).
Monk is also sometimes in the classic "sealed room" mystery genre.
Conan Doyle invented the "suicide made to look like murder" genre in "The Problem of Thor Bridge", and CSI, Law and Order, Jonathon Creek, Poirot and Monk have all borrowed the idea in a modified form at one time or another.