New York’s pied-a-terre tax rollout was blocked for a second time by a Staten Island judge who said the city improperly published property information and wrongly required homeowners to apply for exemptions.

New York State Supreme Court Justice Wayne Ozzi in Staten Island on Tuesday granted a request by the homeowners for an order requiring the city to take down a supplemental roll of more than 900,000 properties that could be subject to the tax and replace it with a more limited list.

Ozzi issued a similar ruling in August, but the city was able to quickly get an appeals …