What are the regulations regarding the safety briefings and harness designs for open-door helicopters?
The flight was a "doors-off" photographic "experience" conducted by a company called FlyNYON, as seen in this video. The doors of the helicopter are either removed completely or latched in the open position, and the passengers are secured with tethered harnesses which allow them to sit or stand in the open doorway whilst in flight. Unfortunately, the harnesses used by FlyNYON do not have any quick-release mechanism (supposedly because of the risk of suicides) and so the only means for a passenger to free themselves from the harness is to either undo the carabiner-type shackle in the middle of their back or cut through the harness with a knife! 

Note: FlyNYON operate these flights as chartered "photographic missions", not as tourist/sightseeing flights which would require quick-release belts and harnesses.



Helicopter harnesses ‘did too good a job,’ trapped crash victims underwater  


  All of the victims were upside down and wearing tight-fitting safety harnesses when rescue divers found them trapped dozens of feet underwater inside the capsized chopper, FDNY Commissioner Daniel Nigro said.


When a Device Meant for Helicopter Safety Becomes a Death Grip  


  The helicopter that crashed was owned by Liberty Helicopters and flown by FlyNYON, a company that specializes in doors-off helicopter photo tours. The company promoted its safety standards on its website and singled out its “proprietary eight-point Safety Harness System” worn by passengers. It is a complicated system of straps, carabiners and an emergency blade for cutting it off in case of trouble.


Doors-Off Helicopter Flights Under Scrutiny After East River Crash



(Update)
FAA statement on 16 March 2018  


  Helicopter operators, pilots &amp; consumers should be aware of the hazard from supplemental restraint devices during an emergency evacuation during “doors off” flights. The FAA will order operators &amp; pilots to take immediate action to control/mitigate this risk. Until then, the FAA will order no more “doors off” operations that involve restraints that cannot be released quickly in an emergency. Additionally, the FAA will conduct a top to bottom review of its rules governing these flights to examine any potential misapplication that could create safety gaps for passengers.