The Alpine Group Ltd has been charged in relation to a crash on October 18, 2018, which killed pilot Nick Wallis (38) and Department of Conservation employees Paul Hondelink (63) and Scott Theobold (59), both of Twizel.
The brothers were the two youngest sons of Sir Tim Wallis.
An interim report by the Transport Accident Investigation Commission into the October crash, published in December 2018, found a pair of over-trousers flew from the cabin of the Hughes 500 and became entangled in the tail rotor.
That caused the helicopter to crash shortly after taking off from Wanaka Airport.
Appearing by audiovisual link in the Queenstown District Court before Judge John Brandts-Giesen, the CAA sought for three weeks to be set aside for a judge-alone trial.
Directors of The Alpine Group are Jonathan and Toby Wallis, along with Murray Valentine and Angus Wilson.