If you're the mayor and you want to close an airport, do you follow FAA procedure and give notice to the government and all the aircraft owners (especially the ones with planes parked on the tarmac)?
Nope! You shut it down in the middle of the night and bulldoze the runway. Problem solved!
Not necessarily.[1] Also, Illinois law doesn't give local police state-wide jurisdiction. (Some states, including California, do, but Illinois does not.) Unless they're off-duty Chicago cops, they don't have any more authority than ordinary rent-a-cops. They could be charged with assault and battery.
However, this is Chicago. Locals know to never assume anything about city government because you'll tend to discover the opposite later on.