At the new playground on the Upper West Side, children clamber over a rocket-shaped jungle gym, spin on a tire swing and splash and scream among water sprinklers.

It is hard to believe that the scene is anything other than New York City at its summer best. The playground, however, is at the center of a controversy over questions of race and privilege in one of Manhattan’s affluent, liberal neighborhoods.

The turmoil was prompted by a simple question: Who should be allowed to play there?

The playground, which was recently reopened after an extensive makeover, is part of a 60-year-old public housing complex known as the Stephen Wise Towers and is nestled at street level between two tall apartment buildings.

People who think everyone should be allowed to play there want it to reflect what they believe New York City should be known for: incredible diversity and a spirit of openness. But some residents of the housing development want the park, which is legally private property, to be exclusively for them and their children, and they resent others who take up the space.

The renovations, which included repairing a set of horse sculptures made in 1964 by the Italian modernist Costantino Nivola, had delighted both Wise residents and others living in a neighborhood of brownstones and luxury condos and apartments.

Now, those groups seem increasingly at odds. Some neighbors from the surrounding blocks have argued that the renovated playground should be open to all because the New York City Housing Authority — and the upkeep of its properties — is mostly funded by the public. But people who live at the development, who are mostly Black or Latino, say that white and wealthy outsiders are being disrespectful.

Sierra Byrd, who has lived in Wise Towers for 31 years, takes her grandchildren to the playground sometimes. She said nonresidents, who had avoided the development for years, had swamped the playground and stoked the conflict with the Wise Towers residents, even though residents pay rent to live in the complex.

“They play with their color,” she said. “They don’t play nice.”

Building officials recently put up signs reading “No Trespassing” and “For Wise Towers Residents Only.” Then the Trinity School, a nearby elite private school, announced that it would stop taking students to the playground for recess.

Residents on all sides complained to the local councilwoman, Gale Brewer, who has not appeared to take a side. She referred questions about the conflict to a letter she sent to NYCHA last month, in which she asked if the playground was “now restricted to Wise Towers residents and their guests.”

NYCHA officials say that the law about the property is clear.

“NYCHA campuses are private property,” said Michael Horgan, a NYCHA spokesman.

Residents and visitors recounted stories of tense interactions between the two groups — including in situations where the visitors weren’t white — that have exacerbated the conflict. One story described a time when a white parent pulled their child away from a Black child. Another story was about how people who visited the playground called the police on public housing residents. And in at least one episode, a dog was brought into the play area, scaring children.

People who live outside the development are also divided. In heated comments on social media, some neighbors said those who use the playground over residents’ objections are acting entitled when they treat it as public space. They have noted that Central Park and Riverside Park are both about a quarter mile away.

Those who visit the playground defend themselves by saying that everyone benefits when children of different backgrounds play together.

“I don’t know what’s right,” said Marian Goldberg, who does not live in the development but was sitting in the park on a recent afternoon watching her granddaughter play. Ms. Goldberg had walked in past the signs but thought it was OK since the playground seemed underused. “I feel very confused,” she said.

The Wise Towers, completed in 1965, take up a large city block between 90th and 91st Streets. Almost 750 people live there, according to NYCHA. Wise, like other public housing developments, fell into disrepair over the years.

In 2021, the development was shifted over to private management as part of a contentious plan, known as PACT, to finance repairs for public housing through a special pot of federal dollars.

The playground was landscaped and new play equipment was added. The horse sculptures, many of which had chipped noses, were fixed.

The park’s popularity exploded.

“It was just packed,” Ms. Goldberg said. “But it did not look like it was the Wise Towers folks.”

The park is separated from the street by a small, unlocked gate — anyone can walk in. Ms. Goldberg said she liked how the apartment buildings channeled the breeze and how the park felt spacious and safe.

She said she had been living nearby since the late 1990s. Before the upgrades, she said, the park was “raggedy.” Now, she said, it is a “beautiful playground.”

It is not clear if this type of situation — where throngs of nonresidents flock to a NYCHA property — has happened before. As more developments receive similar upgrades, particularly in more affluent areas, it could become something the agency has to deal with.

NYCHA is a public benefit corporation that is not technically part of the city or state government, though the New York City mayor appoints all the members of its board. As a result, NYCHA has control over its land.

Mr. Horgan, the spokesman, said that the agency supported “Wise Towers’ residents and their desire to restrict use of the space to residents of the development and the property managers’ signage to notify nonresidents that the courtyard is not a public space.”

Tom Corsillo, a spokesman for the PACT Renaissance Collaborative, which manages the building, said in a statement that the Wise Towers residents were “our top priority” and that “it has been a privilege to help make their homes, including their outdoor open space, a place they can be proud of.”

Kevin Ramsey, a spokesman for Trinity School, said that the school would abide by the signs restricting access to the playground. He added that the school was “recommending that members of the Trinity community do the same.”

On the recent afternoon, Ms. Byrd sat among a group of Wise Towers residents near the entrance of the playground, watching as people paused in front of the “no trespassing” signs affixed to the fence. Ms. Byrd or others from her group confronted a few people who walked in, asking if they lived in the development.

But mostly, the residents said they had started to avoid bringing their own children and grandchildren to the playground because it was too crowded.

Ana Delcroix, who lives near 86th Street and Columbus Avenue and brings her daughter to the playground, said she had been stopped by residents as she was walking in. She had told them she was meeting someone inside.

She said New York City, in particular, should be a place where people of different backgrounds and cultures mixed.

“That’s what we’re known for,” she said. “We are not exclusive — ‘This is ours, this is yours.’”

Ms. Delcroix stood next to Lisa Mosley, whose 8-year-old granddaughter attends the same school as Ms. Delcroix’s daughter. Ms. Mosley does not live in Wise, but uses a housing voucher to help pay her rent. She said that “kids come from all over” to play on the playground, and that it shouldn’t be restricted.

Shein Little, 39, and Shona Hairston, 35, agreed. The couple lives in a nearby public housing development, the De Hostos Apartments, and had brought their children to the park on a recent Saturday.

Mr. Little said that if the playground were on a private development “it would be locked up.” But he said he thought it should be a “public place.”

“The sign says what it says,” he said. “But it’s not a private park.”