The statue on the roof is actually a more decorative and elaborate "flag," in a manner of speaking. You can see many of these on farmhouses, usually with a rooster as the object along with directional "forks" for North, East, West and South. To steal info from the internet: A weather vane is an instrument for showing the direction of the wind . They are typically used as an architectural ornament to the highest point of a building. This one is attached firmly in place...I wonder if the city just got cheap and bought one that looked like a real masterpiece, figuring no one would really notice at that height!?
I was looking over pictures of the Leinster House that you mentioned...whoa, I now wonder if the city of Phoenix also stole the design...amazingly similar! Always love the comments, thanks for writing so often! Hope you have a great weekend...and get some sun! ha