Women who walk around Times Square in New York City wearing nothing but paint over their breasts have been at the center of controversy the past few weeks.

Mayor Bill de Blasio wants the women — known as "desnudas" or the naked ones — to go. He even threatened to dismantle the pedestrian plazas built in Times Square to make it so.

But de Blasio is facing a complicated legal landscape that is underpinned by a state court decision in 1992.

The story starts on June 21, 1986 when a group of women decided to protest a law that appeared to make going topless illegal.

Here's how the Village Voice described the protest in 2013:

"Ramona Santorelli and Mary Lou Schloss made history at a topless picnic a group of feminists staged for the sole purpose of getting arrested.

"'We chose June 21, the summer solstice,' Santorelli says of the watershed event in 1986. Nine women took off their shirts and waited for police to arrest them. The activists were charged with violating New York state penal law section 245.01, which prohibits exposing 'the private or intimate parts' of one's body. The law went on to spell out a crucial gender distinction: On 'a female person,' said 'parts' included 'that portion of the breast which is below the top of the areola.'"

Santorelli and Schloss challenged their convictions in court. They argued that the Equal Protection Clause of the 14th Amendment made it unconstitutional for lawmakers to ban women — but not men — from going topless.

The court threw out the women's convictions, but they did not go as far as Santorelli and Schloss wanted them to.

Instead, a majority of the court sidestepped the constitutional issue with a narrow ruling. The court pointed to previous decision in 1973 that said that section 245.01 of the penal code, should not be applied to "the noncommercial, perhaps accidental, and certainly not lewd, exposure alleged."

The key word for the fight in Times Square today is "noncommercial." The "desnudas" are walking around topless and also asking for tips after taking pictures with tourists.

Does that make their actions "commercial?" Perhaps. But The New York Times reports there is one more ruling to take into account. The paper reports:

"City officials, however, say arresting the women for indecency is not an option. That is because they can make a strong argument that they are street performers, exempted by the state law and protected by the First Amendment, the officials said.

"Furthermore, the state's highest court also ruled in 1992 that panhandling was a form of protected speech, so unless the women aggressively solicit money, or harass people, they cannot be arrested, the officials said.

"'It's their argument that they are artists, or street entertainers, and not just someone hanging around half-naked,' said Larry Bryne, the deputy police commissioner for legal matters. 'As long as they are performers exercising their First Amendment rights in a lawful way, it's not a criminal law-enforcement issue that we can address.'"

So, it's complicated and Mayor de Blasio has set up a task force, which will report back to him on Oct. 1 on strategies to deal with the "desnudas."

Santorelli, by the way, spoke to the Times yesterday.

Now 57, she told them she was not surprised that "the patriarchy" was trying to stop the "desnudas."

"Women's breasts," she told the paper, "are very, very powerful."

It's worth noting that tonight's All Things Considered will take a look at a protest of about 20 women who went topless on Hampton Beach, on the New Hampshire coast, on Sunday. Click here for your local NPR member station.

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