Here is a New York Times report on the order and here is a PDF of the underlying complaint in the case. The theory of the complaint seem to be administrative and procedural: The underlying statute directs the city to make an “initial determination” that a property is not a primary residence for purposes the tax, but (the plaintiffs argue) the city has inverted that process by asking certain homeowners to affirmatively prove that their properties are primary residences. From the Times:

The tax is levied as a surcharge on an annual property tax bill and applies to condos and co-ops that are used as second homes and have a “market value,” as determined by the Finance Department, of at least $1 million. It also applies to one-, two- and three-family homes with a “market value” of more than $5 million.

The homeowners had argued that New York City officials should have worked harder to determine, using existing records, who might have to pay the tax before publishing a data set on the Department of Finance’s website listing homes that “may be subject to the charge.”

That data set contained nearly one million properties.