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.