WASHINGTON — As Mitt Romney campaigned in a restaurant in New Hampshire on Monday, he approached a man seated at a table and said hello. The man, later identified as Al Michaud, replied: “I’m one person who will not vote for a Mormon.”

If Mr. Michaud is alone, Mr. Romney has nothing to worry about. But what if he isn’t?

As the former Massachusetts governor, who is seeking the Republican presidential nomination, gains ground in his bid for the White House, a key question of his campaign will be how he addresses the tenets of his Mormon faith, some of which differ starkly from other religions common in America. Those include a history of racial (until 1978) and gender stratification, as well as the belief that God appeared in human form to the prophet Joseph Smith in the 19th century and that Jesus Christ will eventually return to rule in Independence, Mo.

The Founders of America were exceptionally emphatic in prohibiting the imposition of a religious test in government appointments, issuing, in Article VI of the Constitution, the prohibition that “no religious test shall ever be required as a qualification to any office or public trust under the United States.” Yet the mere question of Mr. Romney’s faith has divided scholars and political commentators. Some argue that he will have to confront the issue directly, while others say it is plainly unfair, and even un-American, to scrutinize the religious beliefs of a presidential candidate.

More than it has for either of his top rivals for the Republican nomination, Mayor Giuliani and Senator McCain of Arizona, Mr. Romney’s faith has played a central role in his life. Before enrolling at Brigham Young University, he spent 2 1/2 years in France as a missionary for the Church of Jesus Christ of Latter-day Saints, as the church is officially called. He later held a leadership position in the church, serving as president of a stake — similar to a diocese in the Catholic Church — in Massachusetts, during which he oversaw about 3,000 members.

Mr. Romney, 60, is not shy about his faith, nor does he advertise his membership in the church.

While he has said he “absolutely” believes in his faith and is proud of it, he discusses specifics only selectively. Of the well-known practice of polygamy, which the church repudiated in 1890, he said recently on “60 Minutes”: “I can’t think of anything more awful than polygamy.”

In an appearance last month on “The Tonight Show,” he described his reaction to the church’s edict reversing the long-standing prohibition on ordaining blacks to the priesthood: “I remember the day that that changed — I pulled over to the side of the road and literally broke down. It was so important to me to see that change in my church.”

Mr. Romney says he follows church policy in tithing 10% of his income and abstaining from alcohol, drugs, and coffee. He has declined to say whether he wears the sacred undergarments — usually white-colored underwear worn over the torso and upper legs — required of church members. (Scholars of the religion generally assume he does.)

The Church of Jesus Christ of Latter-day Saints began in 1830 with a membership of six, including Joseph Smith. According to the faith, God and Jesus Christ appeared in the flesh to Smith and directed him to a hillside in upstate New York, where he recovered an ancient record engraved on tablets. Within three months, he translated the tablets into the 500-page Book of Mormon. The religion had grown to 26,000 members by 1844, when Smith and his brother were killed by a mob. Though the church is now based in Salt Lake City, Utah, its scripture places the Garden of Eden near Independence, Mo., and Mormons believe that is where Christ will one day return.

Mr. Romney’s campaign said he was unavailable to be interviewed for this article. When asked about specific teachings of the Book of Mormon, in interviews and on the campaign trail, he usually sidesteps, referring questions about doctrine to the church itself. He has also used humor. “The most unusual thing in my church is that we believe there was once a flood upon the earth and that a man took a boat and two of each animal inside the boat and that he saved humanity by doing that,” Mr. Romney said on the “Charlie Rose Show” last year, using the story of Noah’s ark to illustrate the point that Mormonism is no different than other religions in sharing beliefs that some may consider odd.

The last Latter-day Saint to make a serious bid for the presidency was Mr. Romney’s father, George Romney, who sought the Republican nomination in 1968. But observers more frequently compare the candidacy of the younger Romney, who is leading his competitors in fund-raising and rising in some key state polls, to that of John F. Kennedy in 1960.

Facing skepticism about his Catholic faith, Kennedy delivered what is now considered a landmark speech in Houston, in which he reaffirmed his belief in the separation of church and state and declared that no Catholic prelate would tell an American president how to act.

The membership of the Latter-day Saints has since grown to nearly 6 million nationwide, with more than 12.5 million members across the globe. Its most prominent elected official is Harry Reid, the Senate majority leader and a Democrat.

Five months into Mr. Romney’s campaign, a debate is ongoing among religious scholars and political observers over how he should handle “the Mormon question.”

To some, incidents like the one involving Mr. Michaud in New Hampshire suggest that Mr. Romney should be proactive. There have been other, less-publicized efforts to derail his candidacy. The leader of Florida-based Bill Keller Ministries, Bill Keller, wrote on its Web site, liveprayer.com, last month that a vote for Mr. Romney would be a vote “for Satan.” That led a religious freedom group, Americans United, to urge the Internal Revenue Service to investigate the ministry for violations of tax law.

“It’s persistent. The Mormon issue, or the religious issue, for 2008 has not gone away,” the co-author of “Mormon America,” Richard Ostling, said. “That tells me he needs to address it in some comprehensive way.”

But for others, the idea that Mr. Romney will face questions about his beliefs is repulsive. “Candidates ought to be asked about tax policy, Iraq, Iran, things like that, not the details of their theology,” a conservative commentator, Hugh Hewitt, said. Mr. Hewitt has written a book, “A Mormon in the White House?” that essentially makes the case for why Mr. Romney’s faith should be a nonissue in the campaign.

“That sort of line of questioning has never been anything other than utterly reprehensible in American political discourse,” he said. “It’s a not very subtle way to stir the pot of religious bigotry.”

The common perception is that Mr. Romney’s faith will give him more trouble in the Republican primary, where evangelical Christians may be skeptical of Mormonism, than in the general election. Some evangelicals do not consider Latter-day Saints “Christians,” although Mormons consider themselves to be. Mr. Romney has courted evangelicals, focusing on their shared conservative views on abortion and same-sex marriage.

Yet the church’s history on race and gender may also pose problems. Although the Mormon leadership, through a “revelation” in 1978, did allow black males to be ordained, it has not changed passages in its scripture teaching that “a skin of blackness” is a curse from God. Mr. Ostling writes in “Mormon America” that the references pertain to American Indians, rather than African-Americans.

He and other scholars point out that the church has made considerable strides since 1978 in reaching out to blacks, increasing membership both in Africa and in predominantly black communities in America, including Harlem.

Like other denominations, notably Roman Catholicism, the Latter-day Saints do not ordain women, although women are active in church activities. “That’s been a part of their theology, as well, and it’s not likely to change,” a noted scholar and author on Mormonism, Jan Shipps, said. “I’m not sure it will ever change. But I’m not sure it will ever change for Roman Catholics, either.”