In their last days, Saudi-born Rotana Farea and her little sister, Tala, were inseparable.

They stayed together at various Manhattan hotels, went shopping around town — and were even seen praying loudly in Riverside Park.

But their Big Apple trip was a final farewell, not a reckless spending spree.

Shortly after they were spotted in the park, the sisters bound themselves face-to-face with duct tape and leapt as one into the water, ending their lives.

It was a tragic end for Rotana, 22, and Tala, 16 — who in the past year fled an allegedly abusive family in Fairfax, Va., spent eight months in a shelter and then traveled to New York.

At some point along the way they applied, without success, for asylum in the US.

The Saudi Arabian embassy found out and alerted their mother — telling her the family must return to their home country.

That was out of the question for the long-suffering sisters.

“They would rather inflict harm on themselves and commit suicide than return to Saudi Arabia,” NYPD Chief of Detectives Dermot Shea told reporters, relaying what the sisters had told one non-family witness.

The bodies of Rotana and Tala washed up off West 68th Street on Oct. 24 — still bound together — and were spotted by a man exercising in the park. Shea, in a news briefing Friday at Police Headquarters, gave a chronology of the sisters’ tragic final year.

The siblings were last seen by their family, in Fairfax, on Nov. 30, 2017.

Sometime in December, they were located — “but they were not returned to the home,” Shea said.

“They were returned to a shelter-like-type facility, due to some abuse allegations that came up,” concerning their family, he added, declining to elaborate.

The two stayed in the shelter, which Shea did not name, through the summer.

“In the end of August,” he said, “the girls go missing from the facility,” he said.

On Aug. 23 or 24, “We believe the girls took a series of methods of transportation, north-by-northeast, essentially arriving in New York City on or about September 1st of this year,” Shea told reporters.

The NYPD pieced together part of their trip by subpoenaing Uber.

“We have that corroborated by some electronic court records — [obtained through] subpoenas and the like — specifically at least one, where they took Uber cabs towards a path bringing them to New York City,” he said.

Once in the city, the sisters stayed in the kind of hotels where two very young women, traveling alone, would feel safe, including a Hilton, a Hyatt and the Knickerbocker.

“It’s important to note, we have them recovered on video in apparently good health during this time,” Shea said. “As recently as a week before when they were discovered.”

The sisters always ordered their meals, from room service, in pairs, he said.

“Always two meals,” he said.

“We have them shopping at various locations, we have them ordering food and again at the hotels.”

The sisters and their family had been in the US just over two years, Shea said.

At some point, family members told cops, the sisters had applied for asylum in the US, citing family abuse.

The application did not go well — as The Post reported Tuesday, “This is not corroborated at this time from us,” Shea said, “but there are reports of abuse [involving] the brother, the mother and the father that had been brought to our attention.

“This is in another jurisdiction, and this is sometime in the past.”

Then, late last month, the card they were using — a personal card in the elder sister’s name — apparently maxed out.

On their last day alive, a witness came across two young women now believed to be the Farea sisters. He saw them sitting together at around 7 a.m. in a playground between 158th and 163rd streets in Riverside Park, and the image now haunts him, Shea said.

“He came across . . . two girls sitting about 30 feet apart . . . alone . . . they were sitting with their heads in their hands, their heads lowered . . . and making noises that he describes as praying.”

The two appeared to pray together for about 15 minutes, the witness, a man who frequently exercises in the park, told cops Wednesday, after piecing the disturbing sight together with an account of the sister’s death.

“He described them as alone, just the two of them,” Shea said. “They were sitting 30 feet apart, but he believed they were together . . . they were making noises loudly that he described as praying.”

A passerby on the Hudson bike path found their corpses later that day.

An initial investigation centered on identifying the women and ruling out foul play.

“At this point, there’s no credible evidence that any crime took place in New York City,” Shea said Friday.

An autopsy has yet to confirm that the sisters died of drowning, and an investigation is continuing, Shea said. But among the safe conclusions so far is the sisters’ close bond — in death as in life.

The duct tape that bound them was “not binding them tight together,” Shea said. “More like keeping them together.”