The five words tucked into a bill listing the rights of homeless people in New York City seem straightforward enough:

“The right to sleep outside.”

The bill is sitting on the desk of Mayor Eric Adams. If it becomes law, it would seem to answer a question that has become a point of contention in big cities trying to cope with rising homelessness, including New York, where Mr. Adams’s administration takes down dozens of urban campsites each week: Do homeless people really have a right to sleep outside here?

The bill’s sponsor, Public Advocate Jumaane Williams, said that his “Homeless Bill of Rights” does not create any new rights; it just compiles existing ones in one easy-to-find place. He said that while there are rules against sleeping in certain places or in ways that create obstructions, sleeping outside on public property, in and of itself, is legal in New York City simply because there is no law against it.

The bill breezed through the City Council last month by a vote of 47-0, including all six of the Council’s Republican members.

But the question of whether, and when, and where, sleeping outside in New York is legal turns out to be a complicated one — and one that gets to the heart of Mr. Adams’s efforts to restore order in what he says has become a disorderly city. The question also took on new significance this week when the city, its shelter system overwhelmed by migrants, went to court to seek a waiver from a decades-old requirement that it offer a shelter bed to everyone who wants one.

Mr. Adams had 30 days to take action on the bill. If he does not approve or veto it by Saturday, it automatically becomes law.

On any given night, several thousand people bed down in New York City’s streets and subways, but the city has a relatively small street homelessness problem compared with many cities in the Western United States that have extensive tent cities and shantytowns.

A 2018 decision by the U.S. Court of Appeals for the Ninth Circuit, which covers nine Western states, effectively bars cities from enforcing camping bans if they do not have enough shelter beds available for everyone who needs them. Cities including Portland, Ore., and Culver City, Calif., are trying to address the crisis by opening municipally run campsites while restricting camping elsewhere. Los Angeles has outlawed tents within 500 feet of schools and banned lying down or storing belongings in places that block the sidewalk.

In New York City, there are many rules on the books that have been used to restrict sleeping rough.

One is a piece of sanitation code that makes it unlawful to leave “any box, barrel, bale or merchandise or other movable property” or to erect “any shed, building or other obstruction” on “any public place.”

The rule was created to address “the ever increasing number of abandoned cars in the City of New York” and “punish those persons who abandon and/or remove component parts of motor vehicles on public streets.” But a federal judge in 2000 upheld the city’s right to apply it to homeless people sleeping in cardboard boxes.

In city parks, it is illegal to “engage in camping, or erect or maintain a tent, shelter or camp” without a permit, or to be in a park at all between 1 a.m. and 6 a.m. unless posted rules state otherwise.

And on the property of the Metropolitan Transportation Authority, both underground and in outdoor elevated subway stations, it is a form of banned disorderly conduct to “sleep or doze” in any manner that “may interfere” with the comfort of passengers. Nor may subway riders “lie down or place feet on the seat of a train, bus or platform bench or occupy more than one seat” or “place bags or personal items on seats” in ways that “impede the comfort of other passengers.”

Beth Haroules, a lawyer for the New York Civil Liberties Union, said that someone who did not violate any of those rules — say, someone who set a sleeping bag in an out-of-the-way spot under a highway overpass and did not put up any kind of shelter — was legally in the clear, at least in theory.

“Assuming that you’re not creating any obstruction in that public space, there is no bar against your being there and sleeping there,” she said.

But mayors have interpreted the rules against obstructing public spaces broadly, Ms. Haroules said. Mr. Adams has continued his predecessor Bill de Blasio’s policy of conducting frequent “sweeps” of sleeping spots, in which sanitation workers dismantle camps and trash people’s belongings.

Last year, the city conducted over 5,000 such sweeps — averaging more than a dozen a day, according to city statistics obtained by the Safety Net Project of the Urban Justice Center. Usually, the people who are swept set up camp again elsewhere.

Crystal Vails, 54, said she had lived on the streets for 13 years, the last year or so in an unused doorway in the West Village. She said that city outreach workers and the police had come 20 or 30 times and made her move her current encampment, but had never explained what was illegal about it.

“They don’t say, that’s the thing,” said Ms. Vails, a Safety Net Project client whose setup includes a tent, two bags, a shopping cart and a camping mat.

“They say it’s against the law to sleep here,” she added. “No, it’s not — if that’s the case I would have gotten arrested a long time ago and I didn’t.”

The city’s Law Department declined to answer questions about what is and is not legal in the realm of sleeping outdoors.

“Our primary obligation is to advise client officials and agencies,” a Law Department spokesman said in a statement. “Providing legal advice to the media on these topics would not be consistent with that obligation.”

To Mr. Williams, the public advocate, “abuses that are happening all throughout the system” created the need for his bill, which requires the city’s Department of Homeless Services to inform homeless people of 10 rights. They also include the right to complain about shelter conditions without being retaliated against, the right to apply for housing vouchers and the right to be placed in a shelter consistent with a person’s gender identity.

“We are just giving an empowerment tool to homeless New Yorkers so they can self-advocate,” he said.

New York City has always had enough shelter beds, but the migrant crisis has strained the system nearly to its limits. The city’s homeless population has jumped by nearly 80 percent since last May, prompting the city to ask a judge on Tuesday for an exemption from the requirement to shelter single adults and adult families when it “lacks the resources and capacity to establish and maintain sufficient shelter sites.”

Steven Banks, the social services commissioner under Mr. de Blasio, was critical of the city’s request.

“It is hard to see how asking a court to suspend the right to shelter that is secured by the New York State Constitution is a winning strategy,” he said, “because there will be far more people sleeping on the streets if the city’s request is granted, and that is in no one’s interest.”

At a briefing on the city’s plans on Wednesday, Mr. Adams’s chief counsel, Brendan McGuire, said that the city’s intention was “not to get a court order so that we can shut the door and have thousands of people living on the street.”

But when a reporter asked what would happen if the requirement were lifted and a person came to a shelter seeking a bed, Mr. McGuire declined to answer.

The question, he said, was “a hypothetical that depends on how the court case plays out.”