The oil workers died when the Super Puma helicopter plunged into the sea off Shetland on August 23 last year.
The Air Accidents Investigation Branch (AAIB) says it has found no evidence of technical failure in the helicopter, which was carrying 16 passengers and two crew.
The Crown Office is also investigating the case and wants access to the cockpit voice recorder data.
In what is being described as a rare legal move, the Crown is expected to petition the Court of Session with the aim of recovering material which is held by the AAIB.
Blackbox recorders are normally retained by AAIB during safety investigations, but a court can rule they should be handed over if it considers it to be in the public interest.
The crash en route to Sumburgh Airport claimed the lives of 45-year-old Sarah Darnley from Elgin, Moray, Gary McCrossan, 59, from Inverness, Duncan Munro, 46, from Bishop Auckland in County Durham, and 57-year-old George Allison from Winchester, Hampshire.
A memorial service was held at the airport last weekend to mark the first anniversary of the crash.
The families of those who died have been informed of the latest development. No date has yet been set for a Court of Session hearing.
A Crown Office spokesman said: "Following a helicopter crash off Sumburgh on 23 August 2013 in which four people died, Crown Office began an investigation into the cause of the deaths.
"The investigation is ongoing and the families of those who died will continue to be updated in relation to any significant developments."
An AAIB spokesman said: "Regulations allow for the release of this type of information if a court decides it is in the public interest to do so. The court has yet to make its decision in this case."