As a federal commission searches for evidence of voter fraud and many states try to impose new voting restrictions, a city in Maryland may move in the opposite direction: allowing noncitizens to vote in local elections.

In College Park, home to the University of Maryland’s flagship campus, the City Council is debating a measure introduced by Councilwoman Christine Nagle that would give noncitizens — a broad category that includes green card holders, students with visas and undocumented immigrants — the right to cast ballots for the city’s mayor, council members and other local officials.

Startling though it may seem, the proposal has extensive precedent both in the United States and worldwide: Forty states used to allow noncitizen voting, and dozens of countries currently do.

“The mayor and City Council are not deciding national policy,” Ms. Nagle wrote in an email. “We make decisions about trash pickup, snow removal and equipment for the parks. I think we have shared concerns with our neighbors regardless of whether they are U.S. citizens.”

She added: “Our neighbors have children in school, work, pay property taxes and income taxes, and make their home in College Park just like we do. As residents of our community, I think, they also should be able to have a say in electing the city’s leadership.”

From 2011 to 2015, according to the United States Census Bureau, 21.1 percent of College Park’s population was foreign-born. That number includes naturalized citizens as well as the residents affected by the proposal.

Many opponents of such measures say they would devalue citizenship, perhaps leading fewer immigrants to seek it. Others argue that it would diminish the voting process by including people who are not invested in or loyal to America.

“The feedback that I’ve gotten from my residents in District 4 has been almost overwhelming against the proposed change in our charter,” said Councilwoman Mary C. Cook, who noted that her husband and brother were naturalized citizens.

Many of her constituents, Ms. Cook said, believe that before voting, people should “be in the country for a certain length of time so they can acquire a familiarity with the city, the country, the language, and pledge their allegiance to America.”

At a City Council meeting on Tuesday evening, residents voiced opposition and support. One attendee, Larry Provost, said that the proposal “threatens to dilute the meaning of citizenship in our country,” according to The Washington Post. Another, Olivia Delaplaine, said, “These are people who live here and who are affected by decisions this council makes.”

Council members ultimately postponed a vote to Sept. 12. They will meet a week before, on Sept. 5, to discuss whether to put the measure to a referendum in November rather than passing it themselves.

Interactive Feature | Get the Morning Briefing by Email What you need to know to start your day, delivered to your inbox Monday through Friday.

Though the College Park proposal has gotten a great deal of attention, it is not the first of its kind. Ten municipalities in Maryland, mostly in the Washington metropolitan area, have already adopted similar ones; the most recent, Hyattsville and Mount Rainier, did so within the past nine months. San Franciscans voted in November to allow noncitizens to vote in school board elections if they have a child in their district’s public schools.

Four municipalities in Massachusetts — Amherst, Cambridge, Newton and Brookline — have statutes that would allow legal permanent residents to vote, but cannot put them into effect unless the state passes its own legislation.

One reason these policies are disproportionately common in Maryland is that local officials there can implement them without state permission.

Under the Illegal Immigration Reform and Immigrant Responsibility Act of 1996, noncitizens are barred from voting in national elections. However, states and municipalities can set their own policies, and state and federal courts have held that noncitizen voting laws are constitutional.

For a large part of American history, suffrage for noncitizens in local elections was the rule, not the exception. From 1776 to 1926, 40 states allowed it in some form, at some point. When voting was restricted to white, male property owners, citizenship was not the central qualification.

But as millions of people from the southern and eastern regions of Europe — people whom, at the time, Americans did not universally regard as “white,” and whose political views were deemed suspect — flowed into the United States in the late 19th and early 20th centuries, anti-immigrant sentiment drove the country away from noncitizen voting, said Ron Hayduk, an associate professor of political science at San Francisco State University and an expert on noncitizen voting laws.

The repeal of these laws coincided with the enactment of other restrictions, like poll taxes, literacy tests and voter registration requirements. And the return of these laws in scattered municipalities has also coincided with a shift in the way immigrants are viewed.

Recent years have brought a sort of tug of war between more and fewer restrictions on voting. There seems to be a cluster of local efforts to allow noncitizen voting, Mr. Hayduk said — but at the same time, other officials are pursuing strict voter identification laws. And President Trump chose an advocate of those laws to lead the federal commission investigating voter fraud. The intensity of the debate about immigration has led to a bifurcated trend, with policies gaining traction in opposite directions.

Ms. Nagle, the sponsor of the College Park measure, said she understood why some people “feel that voting is a right tied to citizenship.” In fact, she said, she once felt that way, too.

But “about two years ago, someone mentioned that it didn’t seem right for students who are here for a short time to have the right to vote and residents who have lived here many years not have the ability to vote because they are not U.S. citizens,” she wrote in her email. “As I thought about it, I began to think, ‘Why wouldn’t we want our neighbors who live in this community to have the ability to vote?’”

The debate over noncitizen voting speaks to much larger disagreements about the place of immigrants in American society, Mr. Hayduk said.

“The big question is: What’s America?” he said. “Who’s an American? What should America — what are the values that America embodies? What does it mean to be an American? Are we a multicultural, multiracial, open society? Are we more of a white Christian version? That’s partly what’s being asked and being answered in these different ways with different laws, policies, movements.”

“It’s kind of a microcosm,” Mr. Hayduk said. “It’s a window into some of these other conversations.”