ALBANY – In the latest twist in the legally tangled New York City schools funding case, the order handed down yesterday by a state appeals court means that it is ultimately the governor of New York and legislators, not the judicial branch, that will determine how much money is needed to ensure that the city’s students are offered a proper education.

The 3-2 ruling makes it more likely that the next governor, and not Governor Pataki, will be the final arbiter in a case that spans more than a decade, involves billions of dollars in taxpayer money, and does not appear to be over.

In what some were calling a surprise decision, the appellate division of the state supreme court, an intermediate court, ordered the Pataki administration to comply with a prior Court of Appeals ruling that found that the state was short-changing a struggling New York City school district to an illegal degree and mandated that the state spend more money to correct the problem.

Significantly, the court, citing concerns about protecting the separation of powers of government, said it would be exceeding its authority if it sent to the governor a price tag for resolving the case. The dissenting judges characterized the majority’s opinion as too weak and accused the majority of allowing the state government to be in perpetual violation of the constitution.

While the court did not specify an exact sum, it recommended that the city public schools receive a range of additional annual operational aid of between $4.7 billion and $5.63 billion and $9 billion in capital money for construction projects and repairs.

The higher operating figure is the amount of additional aid that a lower court judge, State Supreme Court Justice Leland DeGrasse, last year said the state owed the city public school system so that its more than 1 million students would be offered an education that meets constitutional standards.

The lower figure is the estimate for meeting the standard that Governor Pataki’s administration had proposed. Last year, Mr. Pataki rejected the $5.6 billion amount, which was derived from a recommendation made by a court panel of referees, and appealed Judge DeGrasse’s order.

“Indeed, one of the most crucial facts established by the record is that reasonable minds can differ as to the actual cost of providing the opportunity for a sound basic education within the City schools,” stated the court’s majority opinion. “Where there is sufficient evidence to support a range of numbers, it ill behooves the Court to dictate the result; at that point, more than ever, the issue becomes a matter of policy for the other branches of government to determine.”

The dissenting judges pointed to the fact that it’s been almost two years since the Court of Appeals, the state’s highest court, ordered Mr. Pataki to agree to a funding plan. “Under these circumstances, where the legislative and executive branches of government have repeatedly failed to confront and solve a problem of state constitutional dimension, it is the obligation of the judiciary to assert its historic role,” the dissenting opinion said.

It was the third time the appellate division had considered the case throughout the years of appeals – it had previously sided with the state – and its decision seemed to change the focus of the debate. By refusing to assign a hard dollar figure that would satisfy the Court of Appeals ruling, the court has pushed the dispute further into the political realm and away from the legal.

Perhaps an indication of the complexity of the decision is that both sides in the case declared victory yesterday and neither ruled out an appeal.

Officials at the Campaign for Fiscal Equity, the coalition of parent and advocacy groups and local school boards that brought the lawsuit against the state in 1993, sounded triumphant, saying the decision meant that the state had run “out of excuses” and would now be forced to comply. Mr. Pataki issued a statement saying the “court decision reaffirms the longstanding constitutional principle of separation of powers, and has again made clear that budgetary decisions must be made by the Governor and Legislature, not the courts.”

He said the court’s decision was consistent with the level of funding to New York City schools that was provided in recent budgets. If the lawmakers accept the governor’s school aid proposal, the state will have increased city aid by about $1 billion over the last three years.

Behind the outwardly optimistic public reactions, top players on both sides quietly expressed caution. Immediately after reading it, high-level officials in Mr. Pataki’s budget division questioned whether the appellate division had contradicted itself by declaring that it was inappropriate for the courts to tell the state how much to spend but at the same offering a recommended range.

While saying the court’s decision was surprising friendly, the lead attorney for the Campaign for Fiscal Equity, Michael Rebell, told The New York Sun yesterday that the additional money the state provided in previous budgets was far below what was required by the courts and that it wasn’t clear that the money in the upcoming budget would be sufficient.

If the Campaign for Fiscal Equity finds that Mr. Pataki’s budget falls short, the group has several options. It can wait out Mr. Pataki’s term and negotiate with the next governor. The leading candidate in the governor’s race, Attorney General Eliot Spitzer, a Democrat and the governor’s lawyer in the case, has pressed for a settlement.

The plaintiffs also could call for sanctions, including fines, against the state and Mr. Pataki. And they could ask one of the courts to enforce the judgment and threaten to shut down the school system unless the state pays up.

Leaders in both chambers, the Democratic-controlled Assembly and the Republican-controlled Senate, signaled yesterday that the ruling would not upset budget talks, which are nearing the March 31 deadline.

Mayor Bloomberg, who has been far more vocal about the need for the state to give the city’s schools more capital money than he about the need for more operating aid, did not have an immediate reaction to the decision.

For Mr. Bloomberg, the benefits of the ruling are not entirely clear. On the one hand, the court says the state must increase New York City operating by at least $4.7 billion. On the other, the state in its legal briefs said the city should contribute $1.5 billion toward that sum. Under the state’s plan, the federal government would cover the remaining $1 billion.