WASHINGTON — The Supreme Court on Wednesday returned to a subject that produced a major and closely divided decision eight years ago: how far may the government go in aiding religious schools?

In 2002, in a 5-to-4 ruling, the court upheld a school voucher system in Cleveland that parents used almost exclusively to pay for religious schools.

Four new justices have joined the Court since then, but there was nothing in Wednesday’s arguments to suggest that the issue has become any less polarizing.

The program at issue on Wednesday gives Arizona taxpayers a dollar-for-dollar state tax credit of up to $500 for donations to private “student tuition organizations.” The contributors may not designate their dependents as beneficiaries. The organizations are permitted to limit the scholarships they offer to schools of a given religion, and many do.

The program was challenged by Arizona taxpayers who said it effectively used state money to finance religious education and so violated the First Amendment’s prohibition on the official establishment of religion.

The program was novel and complicated enough that the Court’s decision on the merits might not be particularly consequential. But a threshold question, about whether the challengers have legal standing to sue, could give rise to an important ruling.

As a general matter, plaintiffs who merely object to how the government spends their taxes do not have standing. But the Supreme Court made an exception for religious spending in 1968 in Flast v. Cohen.

Arizona, supported by the Obama administration, said the exception should not apply where tax credits rather than direct government spending were at issue.

“If you placed an electronic tag to track and monitor each cent that the respondent plaintiffs pay in tax, not a cent, not a fraction of a cent, would go in any religious school’s coffers,” said Neal K. Katyal, the acting United States solicitor general.

“Flast recognized a special solicitude for taxpayers when money is taken out of their pocket and used to fund religion against their conscience,” Mr. Katyal said. But that is as far as the exception should go, he said.

That approach, Justice Stephen G. Breyer said, could amount to an end to many challenges to religious spending. “Flast is gone,” he said. “There is nothing more to Flast, because it just happened that nobody had thought of this system at the time of Flast.”

Justice Elena Kagan, who was until recently solicitor general, or S.G., asked whether Mr. Katyal’s position on the standing question meant that the court had been without authority to decide at least six other cases “but somehow nobody on the court recognized that fact, nor did the S.G. recognize that fact?”

Mr. Katyal said it was not unusual for the court to wait to decide a question until it was “teed up and presented to the court.”

Justice Ruth Bader Gins Ruth Bader Ginsburg asked him whether anyone, in light of his position, had standing to challenge the Arizona program.

“The way this scheme is set up,” Mr. Katyal said, “our answer is no.”

Paula S. Bickett, representing Arizona, said the state program did not violate the First Amendment “because it’s a neutral law that results in scholarship programs of private choice.”

But Paul Bender, representing the challengers in the case, Arizona Christian School Tuition Organization v. Winn, No. 09-987, said the dollar-for-dollar nature of the tax credit meant that the scholarship money effectively came from the state.

The difference between the Cleveland voucher system in the 2002 decision, Zelman v. Simmons-Harris, and the Arizona program, Mr. Bender said, was that “religion was not involved in the distribution of the money to the parents.”

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