If a New York City Police Department Aviation Unit helicopter is flying over the Rockaways section of New York City's Borough of Queens they would most likely be monitoring:
A) 470.8375 / 482.4875 (136.5), Special Operations Division (their dispatch channel)
B) 477.1375 (167.9), Zone 27 (the 100 and 101 PCTs dispatch channel)
C) 123.100 (AM), their "Company" channel in case their base or another public safety helicopter is looking for them
D) the appropriate frequency for contact with the air traffic controller covering that Class B air space around JFK International Airport. If my notes are correct, that should be 125.250 (AM)
and possibly 156.800 (csq), Marine Channel 16, and any of the other common Marine channels .
There aren't any Troopers on the ground there (NYC Parks and Recreation Department PEPs, maybe - and with their uniform hats, they might look like troopers) and, as far as other "police" agencies go - there is the MTA Bridges and Tunnels BTOs that work the two spans that connect the peninsula and the rest of Queens, but they are on UHF as well.
Depends on what they are doing when they are flying over the area. (This would apply anywhere in the city):
1) At all times, aviation will use the local air traffic control freq (so they can avoid interfering with arriving and departing aircraft from the airports)
2) If not on an assignment (job), they will monitor the SOD channel for requests for help from "ground" units.
3) When answering a job, they will switch from SOD to the division frequency to speak to a on scene supervisor and get details towards what they are needed for.
4) Once they are on scene, if units such as ESU or Harbor are also on scene, they will all switch to Tac G, so they can coordinate search efforts without tying up the division channel