About 12.45pm Tuesday, the Eagle was circling near Glenvar Rd, where patrol cars, including dog unit vehicles, were parked.
The Herald on Sunday asked police in the bush what they were doing, and one replied, "training".
Senior Sergeant Pete Pedersen of the police dog section later revealed an off-duty handler was taking 6-year-old German Shepherd Zinny out for some exercise.
"He was on a lead in that dense bush area ... and let the dog off to have a comfort stop. And the dog and handler have got separated," Pedersen said.
Zinny was found about 90 minutes to two hours after his handler raised the alarm.
"We called out all the staff that were on shift," Pedersen said. "The dog had just made his way down to the end of the reserve and was hanging around the bottom waiting for his handler."
Pedersen said the Eagle helicopter happened to be in the area. "They were airborne at the time anyway so they came and gave us a hand as well."
Pedersen said it was very unusual for a dog and handler to get separated - "I can't remember the last time it happened."
He said dogs occasionally became disoriented in thick bush.
A TV3 report from 2010 said it took 10 months to train a police dog at a cost of $30,000.
The police website says the dogs responded to more than 30,000 incidents annually.
All handlers were officers with about five years' experience before joining the dog unit.