A prestigious North Carolina private college was under the scrutiny of the state Supreme Court on Tuesday, as lawyers argued whether the institution is too closely aligned with a religious denomination to be allowed to maintain its own police force.

The case involves a woman who was arrested on a street near Davidson College in 2006 by one of the school's police officers. The woman, who was not a student, pleaded guilty to driving while impaired but later appealed on the grounds that Presbyterian-affiliated Davidson's police force violates First Amendment protections against the mingling of government and religion.

For Davidson, a school of about 1,900 that regularly ranks among the country's top liberal arts colleges, the question comes down to campus safety, and a lawyer for the school said the court's decision could have consequences for other religious-affiliated colleges with their own police forces.

"The outcome of this case is of critical importance to Davidson and the other colleges in the state it will affect," said Bradley Kutrow.

Other institutions with historic ties to religious groups and police forces include Duke University and Wake Forest University, although 20 of the 36 members of the North Carolina Independent Colleges and Universities, which includes secular and religious schools, do not have police forces.

A ruling by the court could take months.

A trial court ruled that the Constitution permits Davidson to have a police department. That decision, however, was overturned by a unanimous Court of Appeals verdict, which found that allowing Davidson officers to arrest suspects and enforce state law violated the Constitution. A state law allows the state Attorney General's Office to certify police officers at private colleges, whether secular or religious.

That's why the state is appealing the lower court's ruling. On Tuesday, Assistant Attorney General Amy Kunstling Irene argued that even though Davidson has historic ties to the Presbyterian Church (U.S.A.), the school is independent of church control and doesn't meet the criteria for a sectarian religious establishment that would create a First Amendment problem by maintaining a police force.

"While Davidson does have an affiliation with the Presbyterian Church, that affiliation is separate from its primary mission" of educating students regardless of their religious beliefs, Irene said.

But Davidson's bylaws require 24 of its 44 trustees to be members of the Presbyterian Church (U.S.A.), and further require that at least 80 percent of the trustees must be active members of a Christian church, Charlotte lawyer Allen Brotherton said.

Brotherton represents Julie Anne Yencer, the woman who was arrested by a Davidson officer in 2006. Brotherton told the Supreme Court that the religious mandate for the trustees makes the case fairly clear-cut.

"It's difficult for the state to stand here and tell you that the board of trustees, which is defined by its religiosity, is not a religious body," Brotherton said.

In 1994, the state Supreme Court ruled that Campbell University, a Baptist institution, couldn't have a police force because it violated First Amendment protections. But Irene argued that Campbell was much more clearly a religious institution than Davidson, and said the law ultimately has to be applied on a case-by-case basis.

"It's difficult to draw a bright line in these cases," she said.