WASHINGTON (CNN) -- A divided Supreme Court, debating Wednesday whether public prayer at a New York town's board meetings are permissible, looked at the country's history of religious acknowledgment in the legislature and the court's own traditions.

Two local women -- an atheist and a Jew -- brought suit against Greece, New York, officials, objecting that the monthly public sessions on government open with invocations they say have been overwhelming Christian in nature over the years.

The hour of sharp oral arguments presented another contentious case over the intersection of faith and the civic arena. The court's conservative majority appeared to have the votes to allow the policy to continue in some form, but both sides expressed concerns about the level of judicial and government oversight over the content presented by members of a particular faith.

"We are a very religiously diverse country," said Justice Samuel Alito, who worried about the town officials articulating binding guidelines on what can be said. "All should be treated equally. So I can't see how you can compose a prayer that is acceptable to all these" religions.

But Justice Sonia Sotomayor worried about the effect on local citizens who choose not to stand and bow their heads when asked during a public prayer.

"Why wouldn't they feel coerced in some way?"

The high court began its public session Wednesday as it has for decades, with the marshal invoking a traditional statement that ends, "God save the United States and this honorable court."

The case is Town of Greece, N.Y. v. Galloway (12-696). A ruling is expected by early summer.