The city’s annual Cannabis Parade wafted pungently down Broadway on Saturday — with cops helpfully ignoring the billowing clouds of acrid pot smoke.

Some 400 marijuana fans, many openly smoking joints, gathered at high noon to march from 32nd Street to Union Square, where a legalization rally turned into an afternoon-long, music-filled smoke-in.

Their buzz was decidedly un-harshed by The Man.

“If they see anyone breaking the law, they’ll arrest them,” an NYPD spokesman said from Police Headquarters.

But at the rally itself — where participants waved “Legalize It” posters and a few more exuberant stoners cavorted in giant joint costumes — the cops adopted a tacit all-toke, no-action policy.

“We have zero arrests, and we don’t plan on having any,” one sergeant told a Post reporter.

Advocates praised the cops’ mellow take on toking as the latest sign New York was inching toward decriminalization.

Last month, Brooklyn District Attorney Ken Thompson warned the NYPD in a memo obtained by The Post that his office would no longer prosecute people caught possessing — or even smoking — marijuana in public.

“Civil disobedience has long and noble history in this country,” said state Green Party Co-chairman Michael O’Neil.

“For those people who are smoking weed openly, who choose to show their allegiance that way, I think that’s very courageous,” said O’Neil, 34.

Still, having so many cops around made some paradegoers a little paranoid.

“I’m still a little wary of what I’m doing right now,” conceded Rico Valderrama, 38, who traveled to the rally from Washington, DC.

Explaining why he wasn’t lighting up, a 28-year-old real-estate developer from Park Slope said: “Smoking weed is something that’s supposed to be relaxing. If you’re paranoid about getting stopped, then it sort of defeats the purpose.”

Many of those at the rally said they were boosting pot for its medicinal value.

Jolanda Simon, 62, said pot smoke helped her post-traumatic stress disorder.

“It helps me relax and see things more clearly. I’ve been doing it for 30 years,” Simon said.

“The worst they can do is tell me to put it out. They’re not going to arrest me for smoking a joint.”

Kevin William Eastwood, 24, said marijuana helps him live with the traumatic brain injury he suffered from a car accident in July 2012.

“I have to smoke just to get out of bed,” Eastwood said. “We’re supposed to be a free country. How is it free if we can’t have access to this plant that is so magical?”

The origins of the parade are shrouded in as much mystery as smoke.

But organizer Noah Potter said, “It’s been going for at least 40 years.”