The dialogue is from the finale of the 'Columbo' episode "DOUBLE EXPOSURE".
However, if I was ever going to dream up some fanfic for 'Columbo' in which he met one of the incarnations of the Doctor, I would have teamed the Lieutenant up with Sylvester McCoy as the Seventh Incarnation of the Doctor. The Doctor just couldn't ever be the murderer.
No, it would have to be some new alien as the murderer. Perhaps a shape-shifter only looking like a human. And female - a shapely shape-shifter. Someone who had been living on Earth for years, hiding in plain sight, and forced to kill the one who discovered her secret.
If you want to take a stab at that story line, have at it! I would just like the chance to read it.