Police in the Big Apple use every technique at their disposal – including DNA – to solve horrendous crimes in the nation’s largest city.

Even when New York’s cops play fast-and-loose with the constitutional rights of residents. Even when they conduct large “fishing expeditions” that lead to legitimate allegations of racially biased policing.

In this latest battle of public safety vs. privacy rights, the department fared miserably. New York police officials deserve this scrutiny, because practices there could be a roadmap for scores of smaller law-enforcement agencies around the country.

Here’s what happened, according to news reports: Police were desperate to solve the August 2016 murder and suspected sexual assault of 30-year-old Karina Vetrano, who was beaten to death in a Queens park after she went out on a nightly run. Early on, 100 detectives worked the case, and authorities offered a $35,000 reward for information leading to the killer.

Months later, no prime suspect had emerged. Police, however, did have a key piece of evidence: DNA from the crime scene suggested a black man was the killer. So a high-ranking police supervisor ordered officers to get DNA swabs from 360 black and Hispanic men who police had previously arrested in the Queens neighborhood where the attack occurred.

Ethical and potentially legal problems with the collection became obvious, according to the New York Daily News, which anonymously received a list of the names of 50 of those men.

Several had been arrested for misdemeanors or nonviolent crimes – including minor car accidents. Their ages varied wildly, from the 20s to mid-60s. There didn’t seem to be any pattern except for their race and the general location of the previous arrests. Technically, the request for DNA was voluntary, but also coercive.

Those sought for their saliva may not have known that, without a warrant, they could decline the request. Police can “ask as a question, but make you think have no other choice,” Jeffrey Bellin, a professor at the College of William and Mary’s law school, told me in an interview.

Rebecca Green, another William and Mary law school professor — who specializes in privacy issues — said everyone cares about promoting safety and reducing crime.

“At the same time,” Green added, “as technology marches on, we have to wonder, first of all, whether we need better protections for people, and, second, whether these new technologies have the unintended consequences of discriminating against certain populations.”

Dana  Schrad, executive director of the Virginia Association of Chiefs of Police and Foundation, told me this week that Tuesday she could recall only one similar situation in the commonwealth: the search for a serial rapist in the Charlottesville area.

The crimes began in 1997, and a task force spent years trying to track down the rapist. It also had his
DNA. In 2007, Nathan Antonio Washington pleaded guilty to a series of crimes.

But over the years, authorities had contacted 190 African-American men seeking their DNA, since
victims described the suspect as African-American and “youthful looking.”

One of those men eventually sued over alleged federal constitutional violations, in Monroe vs. City of Charlottesville. The city and police department won in the lower court and the U.S. Fourth Circuit Court of Appeals, and the U.S. Supreme Court denied certiorari.

In New York, individuals among the huge sweep told the Daily News they and their relatives were harassed when police came to their door, sometimes repeatedly. Some said they were embarrassed because neighbors saw officers confronting them. One man’s family reportedly moved because of the heavy-handed tactics.

All the while, hundreds of people were caught up in the investigation. They and their family members – and African-Americans and Hispanics in general – questioned this needle-in-a-haystack approach that had little regard for people who were innocent of the slaying.

I asked NYPD media spokespersons, by email, whether a similar DNA approach had ever targeted white men or women in a major investigation.

It was one of several of my questions the department declined to answer.

Police eventually focused on Chanel Lewis, now 22, based on a tip from a department lieutenant who remembered seeing Lewis, who’s black, at least twice in the predominantly white neighborhood “acting suspiciously.” Detectives then got a saliva sample from him, The New York Times reported. Forensics experts said his DNA matched traces found on Vetrano’s neck and cellphone.

Lewis was convicted in April of the slaying and sentenced to life in prison without parole.

A NYPD spokeswoman said by email that officers collect DNA following the law and established protocols.

“1,400 DNA matches have been made for terrible crimes like rape and murder, and it is an investigative tool that has helped take dangerous criminals off the streets,” Sgt. Jessica McRorie noted.

Sure, but most of those matches probably didn’t come through wholesale, random campaigns of DNA swabs. Nor did police tell me whether they alerted individuals that they could legally decline the collection – though we all know the answer.

The broader issue is troubling: Why should police be able to harass people who have done nothing wrong and in circumstances where police don’t even have to provide the probable cause necessary for a warrant?

We all want criminals off the streets, but the procedures should be clear. I mean, if we wanted to make things really air-tight, we could start collecting DNA swabs of infants as they come out of the womb. Just in case.

No one favors such an egregious policy.

This isn’t the lone privacy-rights controversy that’s emerged recently. San Francisco this month banned the use of facial recognition technology by police and other city agencies. Civil libertarians have complained about potential abuse by government and increasing surveillance.

More than a decade ago, Virginia Beach ended an error-ridden, facial recognition program at the Oceanfront, after it didn’t lead to any arrests.

I’m not saying “no” to technology. I’m saying “yes” to due process, privacy and the right to be left alone.