It is understood a shooting incident took place at the Te Toto Gorge, near the Karioi Summit Track at Raglan.
Police are appealing to members of the public for any information.
They say the stolen vehicle - a White 2017 Toyota Hiace ZL registration KWF362 - was driven from Whaanga Rd to Gordonton Rd this morning. The 80km journey takes about 75 minutes to drive.
Stacey Davis, executive general manager for rental operations in Australia and New Zealand at Apollo Motorhome, said Apollo was aware one of its rental campervans was involved.
"We're aware of the incident that involved one of our campers in Waikato," she said.
"We are cooperating with the authorities as the investigation continues and our thoughts are with the family at this time."
Police were conducting inquiries to establish the circumstances of the death, Inspector Graham Pitkethley said.
"If you think you have seen this vehicle or have information that may be helpful please contact Hamilton Police on 07 858 6200."
Earlier, at least four police cars, an ambulance and several armed officers had blocked off the corner of Puke Rd and Gordonton Rd around 9am.
One person said on Facebook a white campervan was parked off Puke Rd, a short distance from the intersection.
A spokeswoman for St John said they were called to the incident at 8.11am and sent an ambulance and rapid response vehicle.
She was not able to provide any more details and said any other inquiries would have to go through the police.
One man told the Herald there was easily a half dozen marked police cars cordoning off the road with flashing lights.
There were armed officers kitted out in black clothing at the roadside, he said. Several blacked out four-wheel-drive vehicles were also on scene.
Onlookers were being waved on by police at the cordon.
Another person said there was a large, dark helicopter hovering over the Gordonton area earlier this morning. It's believed it was the police Eagle helicopter from Auckland.
Earlier, a St John ambulance spokeswoman said they were called to the Raglan incident by police around 3.15am. However, they were stood down shortly afterwards.
A police spokeswoman told the Herald police were conducting inquiries to establish the circumstances of the incidents and no other information was available.
Local chef Colin Chung, who lives in Whale Bay, said he heard a helicopter about 6.30am.
"The only time we get choppers that early is when there's someone lost at sea ... a surfer [has] gone missing or a boat going down. So I just assumed that was happening."
He said the helicopter was flying up and down the coastline.
"We got a call from a friend of ours ... whose neighbour employs a man from Te Toto Gorge, who said he'd just come to work and ... reported or found where someone was shot. He said he called police."
Chung said from Raglan that two police vehicles passed him on his way out today.
He said residents in the Te Toto Gorge area were being told to stay in their homes.
"Down the coast there - [authorities are] informing everyone to stay indoors, lock up and keep vigilant."
A farmer about 10 minutes away from the Te Toto Gorge lookout said the area was a popular tourist spot.
He said there was no camping allowed, but tourists tended to regularly do so at the site regardless.
A man at the nearby Ruapuke Motor Camp said he heard a helicopter in the area about 7.30am.
A resident about 20 minutes south of the Te Toto Gorge Lookout said just before 8.15am: "We had a big black helicopter fly over our house.
"I've just sent the kids off to school on the school bus and am wondering now if we're safe."
A spokesman for Fire and Emergency New Zealand said they were called to assist police at the scene on Whaanga Rd, Raglan. Further inquiries were referred to police.