It said Mr Tohu had arrived at the park with a group that was participating in park activities, "but we were of the understanding that he was a spectator only".
The flying fox was not operating at the time of the incident.
"The flying fox had been secured and the deceased had not been authorised to access it, or provided with access by park staff.
"The park has strict operating rules and procedures for the flying fox and all other park activities to ensure customer safety. We do not believe this incident would have occurred under normal operation of the equipment," the statement said.
Moses Tohu
WorkSafe New Zealand was investigating the incident.
Mr Tohu's death has orphaned the couple's 6-year-old son who was in the care of extended family.
Mr Tohu was last night lying at his home in Kawakawa, ahead of a tangi at Mangamuka Marae, near Kaikohe.
Niece Peggy Tohu yesterday paid tribute to her uncle, saying he was a humble man who was left a widower after the tragic death of his wife in 2008 shortly after they had married.
Miriam Matene-Tohu died and baby Tewaipuke was seriously injured when a trailer loaded with posts snapped off a truck and slammed into their vehicle.
Despite the loss of his new wife, Peggy said her uncle pressed ahead, caring for others and doing his best to provide for the now 6-year-old Tewaipuke, who was left with life-long injuries following the crash.
"He just got on with his life," she said. "He couldn't dwell on it. He never cried and stuff.
"Uncle Mo was a real humble, loving man. He could never say no."
Peggy said her uncle worked at Opua-based Ashby Boatbuilders cleaning boats. The company was hosting its Christmas party at the AE Fun Park.
Brisbane-based niece Patricia Tohu said whanau across the Tasman had been devastated by the death. "He was such a nice man. He would look after anyone."
She said he would not let anyone touch his treasured dreadlocks.
Family members would fly back to New Zealand for the tangi to honour the much-loved relative.
- additional reporting Herald on Sunday