Just a few weeks back, a local community board said that a small piece of city-owned land on a leafy block in Murray Hill, Queens, could be put up for sale. The surrounding streets are lined with smooth lawns and shingled houses. The spot itself is grassy and dappled with trees. But there is a catch.

The property, which stretches 500 feet long, is only 3 feet wide and runs smack down the middle of a block of homes, through nearly two dozen backyards. There is no access to the street without scurrying across somebody’s tidy front lawn.

“It’s this very thin strip behind a whole row of houses,” said Marilyn Bitterman, district manager of the community board that approved the sale. “They just want to get rid of it.”

Vacant lots in the right part of town can sell for $14 million, for $30 million and even much more, and so New Yorkers have become accustomed to thinking of land as untapped gold mines. But even here, there are properties so irregularly shaped and so unfortunately situated that they are notable not for their value but for their peculiarity — and many of them happen to be owned by the City of New York.