There are a number of circumstances that legally justify a warrantless search. One of them -- I forget the legal phrase that's generally used for it -- is where the officer has cause to believe that the evidence will be destroyed or spoliated during the time it would take him to get a warrant. And unless Columbo kept a cop posted right there in the room (on what basis?), it seems pretty obvious that the body would have disappeared within minutes after Columbo went out to get his warrant.
Still, the broader point is well taken, that "Columbo" stories sometimes take liberties with various laws -- especially the laws of probability!