New Zealand First says prison guards failed to follow correct procedure when they discovered a prisoner dying at Mt Eden Prison on Thursday morning.
The party's Corrections spokesperson, Mahesh Bindra, said he had been told no Corrections staff were on duty overnight - despite the Government saying the department had resumed management of the prison after failings by the private operator Serco.
The staff that were on duty were inadequately trained, he said.
"What they did was - instead of laying the person in a recovery position and providing first aid - they actually transported that person to a hospital, which was a no no.
"And the police investigating this case are not very happy about it."
Mr Bindra said Serco's contract should be cancelled and the Minister should resign.
Corrections has strongly rejected the allegation.
It said Corrections staff were on duty at night, normal rosters applied, and all incidents were immediately reported to the acting prison director.