At my class C airport there are at least three helicopters based on-field, including a NY State Police helicopter. All are located on the south side of the airport, whereas the scheduled airlines are located north of the main runway.
To depart, these pilots will call tower directly and request a VFR departure in some direction, for example "Grey Rider One (this is the State Police callsign), VFR departure to the south at or below 1,500 feet." Tower will normally respond something to effect of, "Grey Rider One, remain south of runway 10/28 at all times, departure to the south approved. Cleared for takeoff from taxiway Hotel."
The helis, who had hover-taxied from the non-movement area to the hold short line of the taxiway just before making their call, will then hover-taxi onto the taxiway and lift off while remaining above the taxiway.
I have also seen the State Police helicopter depart right from their portable trailer that they use to move the aircraft into and out of their hangar.
LiveATC used to have a La Guardia tower feed and there were a lot of police and news helicopter traffic that could be heard there. These days, you might be able to catch some traffic on the JFK Tower feed.
In terms of VFR freedom, I believe (as I am not a certificated heli pilot) they mostly operate under the same rules as VFR fixed wing with the exception of how low they can fly (helis much lower legally than VFR fixed wing) and their visibility/cloud clearance requirements (again, much lower than VFR fixed wing).
There are IFR helicopter operations, too, but I know even less about their nuances.