Hogan refers to a "high school production of ARSENIC AND OLD LACE". AOL was in its Broadway run until 1944 at which time it transferred to regional productions. High schools could not use the property until the early 1950s at the earliest. As an interesting aside, Robert Crane would play Mortimer Brewster in the 1969 made-for-television version of the play.
What Hogan says is that they are not going to run the production "like a high school production of Arsenic and Old Lace". He's referring to the Broadway production, not an actual high school version. Essentially, he's saying that he's not going to run things like an amateur production of the professional show.