The cockpit voice recorder from the accident off Shetland in 2013, in which four people died, was recovered by the Air Accidents Investigation Branch.
A judge ruled it was in the public interest and the interests of justice to make it available.
The British Airline Pilots' Association (Balpa) said it had lodged an appeal.
The  union's general secretary, Jim McAuslan, said: "The 2013 Supa Puma accident was tragic, and it is vital the AAIB gets to the root cause and has access to whatever data it needs.
"However, providing the data to the prosecutor and the police in parallel to the AAIB's investigation cuts across everything pilots and the broader flight safety community stand for.
"We cannot stand by while the court allows that to happen without pursuing other legal avenues to highlight our concerns and question whether it is the correct approach."
Prosecutors have been trying to establish whether anybody could be held criminally responsible for the crash.
The Air Accidents Investigation Branch (AAIB) has the right to initial access to the cockpit voice recorder but it routinely chooses not to hand over the material to other bodies - in this case the Crown prosecutors.
The BBC Scotland news website revealed last year an order was being sought by Lord Advocate Frank Mulholland QC at the Court of Session to access the data.
It was a rare legal move.
Lord Jones said he was satisfied that disclosing the data would have no adverse impact on current or future crash investigations - but that it could only be disclosed to the Crown Office and Police Scotland.
A total of 18 people were on board when the Super Puma crashed on its approach to Sumburgh.
Helicopter passengers Sarah Darnley from Elgin, Gary McCrossan, from Inverness, Duncan Munro, from Bishop Auckland, and George Allison, from Winchester, lost their lives.
A ruling that investigators should hand over the black box from a North Sea helicopter crash to Scotland's top law officer is being challenged.