The Manhattan district attorney’s decision to charge a white woman with filing a false police report against a Black man in Central Park does not have the support of one key person: the victim himself.

The man, Christian Cooper, has not cooperated with the prosecution’s investigation. The woman, Amy Cooper, lost her job and was publicly shamed after a video Mr. Cooper made on May 25 was posted online; it showed her calling 911 to claim an “African-American man” was threatening her. Those consequences alone, Mr. Cooper said at the time, were in his view perhaps too much punishment.

“On the one hand, she’s already paid a steep price,” Mr. Cooper said in a statement on Tuesday. “That’s not enough of a deterrent to others? Bringing her more misery just seems like piling on.” But he added that he understood there was a greater principle at stake and that this should be defended. “So if the DA feels the need to pursue charges, he should pursue charges. But he can do that without me.”

Mr. Cooper’s decision not to cooperate may present some challenges for prosecutors. But it also reflects a wider debate among people who generally consider themselves allies in the growing movement to call attention to and fight racism, not just in policing, but in society.

The announcement that she will now be prosecuted has drawn mixed reactions from Black community leaders and advocates for overhauling the criminal justice system.

Ms. Cooper’s 911 call was seen by many as a clear example of everyday racism and fueled outrage over the dangers associated with making false reports to the police about Black people.

Some social justice advocates said that Ms. Cooper’s case should serve as a warning to others who might seek to wrongfully use the police in a racially charged encounter. But some argued that charging her criminally reinforces the idea that the only just consequence for wrongdoing should be incarceration.

For instance, Josie Duffy Rice, the president of The Appeal, a nonprofit website, said that bringing criminal charges against Ms. Cooper legitimizes a criminal justice system that she considers to be flawed and racist.

“Ask yourself what criminal charges can do to Amy Cooper that hasn’t already been done?” Ms. Duffy Rice wrote in a tweet, without capitalization and missing some punctuation. “Has she not faced consequences? She did something absolutely horrible and she lost her job, her dog, her personal business was on the front page of the paper.”

The incident on Memorial Day weekend began when Mr. Cooper, an avid birder, was looking for birds in a wild part of the park known as the Ramble, and encountered Ms. Cooper as she walked with her dog off the leash.

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Credit…Brittainy Newman/The New York Times

He asked her to leash the dog. She refused and he began filming. Ms. Cooper said she would tell the police that “an African-American man is threatening my life” before dialing 911.

The video of the encounter went viral on Twitter and garnered more than 40 million views.

On Monday, the Manhattan district attorney, Cyrus R. Vance Jr., announced plans to charge Ms. Cooper with falsely reporting the confrontation, a misdemeanor that carries a maximum penalty of a year behind bars. If convicted, however, she is likely to receive a conditional discharge or be sentenced to community service or counseling. She was ordered to appear in court on Oct. 14.

Ms. Cooper’s attorney, Robert Barnes, has said his client would fight the charge.

Mr. Vance’s decision received praise in some quarters.

“Her racist behavior could have had dire consequences for a Black man,” Mayor Bill de Blasio said on Twitter. “Glad she’ll face consequences of her own.”

Others pointed out that Ms. Cooper’s actions might have had dire consequences and she should be held responsible, regardless of Mr. Cooper’s sympathy for her plight.

“If the police believed she was really being attacked, they could have come in with guns drawn and she would have been the only witness in this — outside of that video that may or may not have surfaced,” said Gloria J. Browne-Marshall, a professor of constitutional law at the John Jay College of Criminal Justice. “This isn’t just about Christian Cooper. The community has been harmed by the actions of Amy Cooper and, in order to rectify this, then the people of New York need to have their day in court, even if Christian Cooper is a reluctant witness.”

Ms. Browne-Marshall said the case was only the latest example in a long history of incidents in which white people have summoned law enforcement and falsely accused a Black person of a crime. Others have compared the case to the 1955 lynching of Emmett Till.

The video of the incident captured on Mr. Cooper’s phone shows Ms. Cooper with a tight grip on her dog’s collar. She says to a 911 operator in a high, frantic voice: “I’m in the Ramble, there is a man, African-American. He has a bicycle helmet and he is recording me and threatening me and my dog.”

Before ending the call, she adds, “I am being threatened by a man in the Ramble, please send the cops immediately!”

Mr. Cooper said in a Facebook post that after the woman refused to leash her dog, he decided to offer the dog treats in an effort to convince her to abide by the leash law.

“Look, if you’re going to do what you want, I’m going to do what I want, but you’re not going to like it,” he told her, before he pulled out the treats and began filming, according to his post.

Alvin Bragg, a former federal prosecutor and a professor at New York Law School, said the video provides sufficient evidence for the prosecution, and that her focus on his race suggests she intended to file a false report, a necessary element to prove a crime.

“There is a false weepy tone and she strategically placed significance on race,” Mr. Bragg said. “She is harping on deep historical issues in our country. She is emphasizing those words and she knows the effect it can have on the listener.”

To prevail at trial, prosecutors will have to prove that Ms. Cooper did not believe in that moment she was being threatened and that she intended to file a false complaint against him, said Daniel R. Alonso, a former chief assistant district attorney in Manhattan.

“A threat can be, ‘I’m going to kill you,’ or it can be subtle,” Mr. Alonso said. “She may well have believed at the time that his statement was threatening in her definition.”

But Marc Lamont Hill, a media studies professor at Temple University who supports defunding police departments, said the case has forced some advocates who want change the criminal justice system to reimagine how justice might be served in this instance. “We can’t criminalize our way out of social problems,” he said.

Mr. Hill expressed doubt that Ms. Cooper’s prosecution might stop other similar incidents. He also said that it might send the wrong message to victims of rape or domestic violence who, after complaining to police, decide not to cooperate with prosecutors and might fear being charged with filing a false report.

Councilman Donovan J. Richards, a Queens Democrat who chairs the public safety committee, said that he was not overjoyed to hear that charges had been brought against Ms. Cooper. For him, the matter was complicated.

“I don’t think any of us are celebrating the fact that she was arrested,” said Mr. Richards, who is Black. “I’m hoping at the end of the day she learned her lesson and that this is a teachable moment for folks — that they can’t just call 911 and put people’s lives in danger just because their privilege is being checked.”

Sarah Maslin Nir contributed to this report.