Which if any local police departments have at least one officer assigned specifically to investigate stalking cases?

Answer 1

The LAPD has a whole division that deals with stalkers. 

Answer 2

Sorry, but you've given me a big laugh. The idea that a police or sheriff's department would have a "stalking specialist" is not realistic. Even a big city wouldn't assign a person to that specific crime.

Answer 3

NONE. There are simply not enough stalking cases for even the largest departments to assign an officer EXCLUSIVELY to stalking cases.