Trustees of tony Gramercy Park have sent a terse e-mail to those lucky enough to have keys to the city’s only private park, ordering them to wear masks during spring strolls since it’s impossible to socially distance along its paths.

Masks or no, some embarrassed residents are buzzing that the park should drop the private shtick and open up to the public during the coronavirus pandemic, and beyond, because it’s “deflating” to the neighborhood.

An e-mail went out to residents of the 39 buildings around the park that are allowed inside its gates with the heading “Why wearing a mask or face covering is mandatory in Gramercy Park, since social distancing cannot be maintained.”

The message, from veteran park warden Arlene Harrison, added, “More people than usual are using the Park paths. People sitting on the benches are only approximately 2 feet away from people using the paths. People trying to pass each other are not able to maintain the 6 feet required for social distancing.”

The e-mail also said, “While front-line workers are sacrificing their own lives for us … the least we can do to slow the spread of this virus is wear a mandatory mask or face covering in Gramercy Park.”

But a resident with a key said some locals have been angling to open up the park for years, and now’s the time. “Seeing firsthand the effect it has on the neighborhood is deflating. Everyone deserves access to this space,” the source said. “Anyone with a heart would open the park during this crisis. Apparently social distancing is already not possible, and masks are necessary, so open the gates and remove the ‘Keep off the grass’ signs so there is more space for everyone.” The park habitué said others also want the “small-minded and exclusive behavior” to be “a thing of the past.”

Residents have been known to include Julia Roberts, Jimmy Fallon, Richard Gere, Ric Ocasek and WeWork’s Adam Neumann. A Gramercy townhouse in 2017 sold for $23 million.

Trustees did not immediately comment.