The justices agreed with parents and teachers who claimed that the Department of Education had violated the law when it presented the budget to the City Council before allowing the Panel for Education Policy, a governing body largely appointed by the mayor, to vote on it.

The justices also rejected the city’s contention that the schools chancellor was able to push the budget through as an emergency declaration — something the city said had been done in 11 of the past 13 years. The argument from the city “supports the conclusion that the DOE is simply avoiding its statutory obligations,” the justices said.

However, allowing the City Council to change the budget this far into the school year would be too disruptive and “have a broad unsettling effect,” they said. In addition, the justices pointed out that the Panel for Education Policy did eventually vote in favor of the budget.

“Even if you’re right, the remedy seems so extreme,” Associate Justice Judith J. Gische said during arguments in September, addressing the plaintiffs. “It’s like putting a tourniquet around your neck for a nose bleed. There were so many more efficient ways to handle this that wouldn’t affect the functioning of a very complex school system.”

Laura D. Barbieri, the lawyer who, along with Arthur Schwartz, represents the parents and teachers, said that she and her clients were gratified that the court agreed with them on the issues raised by their case but were disappointed that there would be no remedies to the budget this year. Still, she said, it is encouraging that the courts put the Department of Education and the city administration on notice for the future.

“It only became apparent and horrific when the budget was cut so drastically,” Ms. Barbieri said. “We took notice and found a way to ensure that the law was followed.”