The majority of the 2296 people questioned said it was enough that the armed offenders squad was armed.
In the survey by the New Zealand Herald, 31 percent of those questioned supported police carrying firearms at all times.
The majority view followed existing police practice where armed police responded to a specific incident and front line police did not have regular access to weapons although airport police were regularly armed and weapons were regularly carried in some police cars.
In the survey 1.2 percent of those questioned said police should not be armed in any circumstances, and three percent were unsure.
The survey, carried out between December 10 and December 17 last year, was before Constable Jeremy Snow wals seriously injured when he walked into a hail of bullets in Papatoetoe as he checked out a suspicious car.
The majority who said no to arming police were influenced by a nostalgia which had no place in the modern world, Police Association president said Greg O'Connor said.
"Unfortunately that nostalgia is less and less in keeping with the realities of the job.
"Criminals don't necessarily arm themselves against police, they arm themselves against each other and police are becoming collateral damage in that," Mr O'Connor said.
He said the arming of the police was inevitable and urged Police Minister Judith Collins to follow the practice in Norway, where police officers were not armed but firearms were carried in all patrol cars.
