Harry is not the actual name of the cop, it's a reference to Alfred Hitchcock's dark comedy The Trouble with Harry (1955).

Movies that comically deal with the problem of getting rid of a corpse are numerous, one classic being Arsenic and Old Lace (1941). Other than that, the number of lesser memorable flicks unfortunately dominates.
Aside from the slapstick humor, my Harry has an additional purpose which will only be revealed much, much later in the story.