The cockpit voice recorder from the accident off Shetland in 2013, in which four people died, was recovered by the Air Accidents Investigation Branch.
Prosecutors have not been able to access vital data to examine whether anyone was criminally responsible.
A hearing is due to be held at the Court of Session in Edinburgh.
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 at the Court of Session to access the data.
It is a rare legal move.
The lord advocate, Scotland's top prosecutor, is seeking the order for disclosure of the voice recorder data recorder under the Civil Aviation (Investigation of Air Accidents and Incidents) Regulations 1996.
Section 18 covers disclosure of relevant records, and the Crown can act if it believes it to be in the public interest.
Helicopter passengers Sarah Darnley, from Elgin, Gary McCrossan, from Inverness, Duncan Munro, from Bishop Auckland, and George Allison, from Winchester, lost their lives.
A total of 18 people were on board when the Super Puma crashed on its approach to Sumburgh.
Scotland's top law officer is going to court to try to get air accident investigators to hand over the black box from a North Sea helicopter crash.