New York City police say no suspicious game is suspected in the deaths of two Saudi Arabian sisters who were found tied together in a band on the Hudson River.
Tala Farea, 16, and Rotana Farea, 22, had previously suggested they would rather hurt themselves than return to their homeland, police said.
Detectives say the girls may have applied for asylum to stay in the US.
A witness says that the siblings prayed before death by the water.
Detective boss Dermot Shea told reporters Friday: "At this point, everything we've seen so far points to something other than a crime."
He said the sisters told the family members they "would rather harm themselves and commit suicide" than to return to Saudi Arabia.
Chief Shea said there were unproven claims that the sisters had fled an abusive home.
A spokesman for the New York City Police Department said there was no evidence linking the Saudi government to her death.
The mystery envelops the US deaths of the Saudi sisters
The police have been investigating the deaths of Farea sisters since October 24, when their bodies were discovered on the banks of the Hudson River in Riverside Park.
Detectives initially suspected that they had jumped off the George Washington Bridge, but changed their theory due to the lack of physical injuries they would have sustained in such a fall.
Instead, they now believe that the girls, with their living waists and ankles loosely taped, walked into the water alive, and that no crime was committed against them that caused their deaths.
According to Chief Shea, an eyewitness reported on Wednesday over a "story that persecutes him."
The man said he was training at Riverside Park when he saw two people, who were probably the sisters who were sitting at a distance of about 30 feet (9 m) near the waterfront.
"They sat with their hands in their heads," Chief Shea said. "Their heads lowered and they made sounds that he called praying."
The police say the sisters arrived in New York City on September 1, "exhausting" their credit cards by ordering meals, shopping, and staying at upscale hotels.
They add that their money was running low at the time of their death.
The siblings moved to Virginia with their mother in 2015, and the older sister was enrolled at George Mason University until last spring.
They were reported missing and taken to a shelter because of abuse allegations.
But in late August, they disappeared again before their bodies were found in New York.
The police are still appealing to all who have met the sisters since August to provide further information.