There are very slight hints of a space police service of sorts in The Red Peri; should I think of them as run by the League, or as company police run by the Interplanetary Corporation?
Later Never mind - I just reread the opening of The Red Peri and realised that Weinbaum describes "a blunt little League rocket" coming to the rescue of a ship after it was attacked by pirates, which I think answers both questions - The League of Nations runs the space fleet!