Just hours later and dozens of blocks south, another passerby would find their bodies on the Hudson’s rocky shore, loosely bound together with duct tape after having washed ashore, police said.

New York City police began to unravel the mystery of what happened to Tala, 16, and Rotana, 22, saying at a news conference Friday that they had no indication the sisters had been killed, even as they await an official cause of death from the medical examiner. The case has generated nationwide attention.

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Chief of Detectives Dermot Shea said the sisters had alleged that they were abused by family members and sought asylum on those grounds in the United States. He said sources in Virginia told detectives that “they would rather inflict harm on themselves than return to Saudi Arabia.”

He added later, “Everything that we’ve seen thus far is pointing to other than a crime taking place.”

Shea said detectives were filling in a murky two-month period after the girls disappeared from Fairfax County around Aug. 23. He said electronic records, including Uber receipts, showed the sisters took various forms of transportation, arriving in New York City around Sept. 1.

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Shea said that over the next seven weeks, they stayed at upscale hotels, including the Knickerbocker in Times Square where rooms rent for more than $400 a night. The sisters were captured on surveillance video appearing with each other and in good health. They went shopping.

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But it soon came to an end.

“The money started to run out — that’s what we believe started to happen,” Shea said.

The sisters were found on rocks beneath a pier on the Upper West Side. They were fully clothed and bore no signs of trauma. Silvery duct tape was wrapped around their ankles and torsos, leading to speculation they might have been killed and dumped.

But Shea said the duct tape was loose, more like it was meant to keep them together rather than bind them. He said police had every indication that the Fareas were alive when they entered the water.

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Shea began the story of what led the sisters to the Hudson over a year earlier, filling in some of the scant details known about their lives. The sisters had little presence online, and no photos of them could be located before police released some this week.

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Shea said the last time family members had seen both sisters was around Dec. 1, 2017, when they left their home in Fairfax, Va. The sisters were found within a day, but transferred to a shelter because of abuse allegations. Shea and Fairfax County police declined to give the shelter’s name, citing privacy restrictions.

Over the next eight months, the sisters lived at the shelter and family members had no contact with them, Shea said. The sisters then left the shelter on Aug. 23 or Aug. 24 and made their way to New York City.

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Shea said detectives had not corroborated the sisters’ allegations of abuse, but they were “between the brother, the mother and father” and were sometime in the past. Shea described the abuse as physical, but it also involved other things he said he would not describe.

Shea said initial reports that the Fareas might have jumped from the George Washington Bridge were likely not true, since their bodies had no signs of a fall from a high place. Likewise, reports that their bodies were found crosswise on top of each other were also inaccurate.

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Shea said he could not confirm a report based on unnamed police sources in the New York Post that the mother of the sisters received a phone call from a Saudi Embassy official who told her she might have to leave the United States because the sisters had applied for asylum. The call reportedly came the day before the sisters’ bodies were found.

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A Saudi official said Thursday that was inaccurate, saying they had only communicated with the mother about her expired immigration status in the United States. For privacy reasons, the Department of Homeland Security said Thursday that it could not reveal whether the sisters had applied for asylum.

The mother of the sisters declined to comment when reached by phone Friday.

“I can’t talk about it,” she said.

Rotana had attended school at George Mason University before dropping out in the spring, school officials said. Tala was a student at Fairfax High School for part of the 2017-2018 school year.

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In 2016, family members were evicted from an apartment in Falls Church, Va., for unpaid rent.

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A woman whose niece attended school with the sisters in their hometown of Jiddah, Saudi Arabia, said they were inseparable and had been hopeful before arriving in the United States.

“They were very much looking forward to going to the US, and had always encouraged my niece to do the same. . . . ‘Study hard and get out to the US!’ ” the woman wrote in a text message.