The city’s policy of barring churches from holding Sunday services in public schools could provide the U.S. Supreme Court with its next big “establishment clause” case, given the fractured judgment rendered by a federal appellate court in Manhattan yesterday.

The three judges on the United States Second Circuit Court of Appeals panel who heard a Bronx congregation’s challenge to the policy each issued a separate opinion. One judge of Bronx House hold of Faith v. Board of Education ruled in favor of the church; another decided in favor of the Board of Education’s anti-church policy; a third found the case was not yet ready for review. As a result, the church may continue to use the school building pending further appeal.

The case likely prompted such division because of the question, more theological than legal, at its center: What is worship? The legal significance of the question hangs on a 2001 ruling by the U.S. Supreme Court, in which the court held that schools allowing use of their campus after hours by secular groups could not then exclude religious groups from conducting religious instruction or discussion on school grounds.

But in the 2001 case, Good News Club v. Milford Central School, the federal high court appeared to draw a distinction between religiously oriented lessons and outright worship, leaving it to federal judges across the country to grapple with whether schools were permitted to ban on-campus worship services. Ruling that such blocks are legally permissible a judge on the Second Circuit panel nominated by President Clinton, Guido Calabresi, declared worship to be a form of speech incomparable to all others. By separating out all worship, Judge Calabresi, concluded that the Board of Education’s policy against it does not discriminate against a particular viewpoint — which would be unconstitutional under the First Amendment — but instead justified the Board’s content-based distinction.

A second judge, John Walker Jr., who was nominated by President George H.W. Bush, rejected that distinction and accused Judge Calabresi of relying “more on judicial legerdemain than judicial reasoning.” “The fact is,” Judge Walker wrote, “that none of us who are judges are competent to offer a legal definition of worship.” Judge Walker said that the Board of Education could not prohibit congregations from gaining access to public schools for worship without violating their First Amendment rights.

Although vehemently opposed to Judge Calabresi’s outcome, Judge Walker seems hesitant of his own conclusion, writing his approach is “admittedly imperfect in this uncertain legal terrain.” The dispute could, Judge Walker wrote, “benefit from a more conclusive resolution” by the Supreme Court.

The case was brought by an evangelical Christian congregation, Bronx Household of Faith, which has been meeting since 2002 at Public School 291/P.S./M.S. 15 in University Heights. The congregation is one of about two dozen that the city says hold Sunday services on public school campuses. An injunction by a U.S. District Court judge currently bars the city from enforcing its anti-worship rule pending the outcome of the Bronx lawsuit, which was filed in 1995.

The city has raised concerns under the First Amendment’s clause regarding the establishment of religion, suggesting that the public could perceive the Board of Education as favoring Christian congregations over Jewish or Muslim congregations because schools typically have the most availability for outside groups on Sunday.

“No child should feel alienated from his or her school for any reason,” a lawyer for the city who worked on the case, Jane Gordon, said. “And that is what’s happening.” But a lawyer for the Arizona-based Alliance Defense Fund, which represents the Bronx congregation, disputed that public school children were under the impression that schools were favoring one congregation or religion over others. “This is an empty government building on a Sunday morning, this is not a public school as such,” the lawyer, Jordan Lorence, said. Given that federal law permits student-led Bible study sessions, Mr. Lorence said there was no logic for the Department of Education to hold so steadfastly to a ban on weekend church services.

“To me there is bit of straining the gnat and swallowing the camel,” he said. The third judge on the panel, Pierre Leval, who was nominated the circuit by President Clinton, ruled that the case was not yet ripe for review, questioning whether the policy has yet to be put in place.

An appeal of yesterday’s ruling could be directed at either the entire Second Circuit or the U.S. Supreme Court.

The appeal of a similar case out of California, which involves a congregation’s intermittent use of a public library, is currently pending before the federal high court, which has not yet said whether it will take the case. But one expert on the First Amendment’s establishment clause, Marc Stern, said that the Supreme Court might prefer to hear the New York case because the congregation in the Bronx has been using the school so regularly for such a long time.

“That makes the establishment clause argument by the city stronger for the liberal side of the Supreme Court,” Mr. Stern, who is the general counsel to the American Jewish Congress, said. “And, if you’re on the conservative side, the case takes in a lot more ground.”