Some counties do regulate when the AC can be turned on and off, but......
This is the first I've ever heard of 'The County won't let us turn it on yet'. It usually in place like California in the middle of summer where electrical demand surges & expensive gas-turbine generators have to turned on, and even then you still might have rolling brown outs.
I'd find out who provides electricity to your area (the city or an independent power company) and contact them. Trust me, they have someone there (if not an entire department) dedicated to knowing every rule & law as it relates to power consumption. They might tell you "Yea, there is this obscure law created back in 1955, but never taken off the books" or "Guy's full of it, what's his name, so we can contact him?"
I also guess you live in an utlities paid apartment? If not, why not turn on the AC? It's not like the apartment complex is paying for it.
Also, read over your lease & any other documentation they gave you when you moved in. It might have a loop hole you can use (or show the loop hole they're using).
Just bought first house a month ago with cieling fans everywhere,