The video provoked widespread shock and condemnation after being shared yesterday.
Police said somebody could have been seriously hurt if the campervan collided with a car coming the the way.
Senior Sergeant Anthony Bond said today the vehicle's registration number had been identified after the rental company contacted police.
The campervan had been returned to the Christchurch airport and police were following up the details of the person who had hired it with the help of the rental company.
"We're following up with the hiree's details and the rental company are assisting us with the investigation."
Snr Sgt Bond said police wanted to speak to the person who filmed the campervan to identify the date and the time.
"All that we've got so far is a video that has been shared by a few people. We want to talk to the person who filmed the original."
