New York City police say no foul play is suspected in the deaths of two Saudi Arabian sisters who were found duct-taped together in the Hudson River.
Tala Farea, 16, and Rotana Farea, 22, had previously suggested they would rather harm themselves than return to their homeland, police say.
Detectives say the girls may have requested political asylum in order to remain in the US.
A witness says the siblings prayed near the water before they died.
Chief of Detectives Dermot Shea told reporters on Friday: "At this point in time, everything we've seen thus far is pointing to other than a crime taking place."
He noted the sisters had told family members they would rather "inflict harm on themselves and commit suicide" than go back to Saudi Arabia.
Chief Shea said there were unsubstantiated claims the sisters had fled an abusive home.
A spokesman for the New York Police Department earlier said there was no evidence linking the Saudi government to their deaths.
Police have been investigating the Farea sisters deaths since 24 October when their bodies were discovered on the banks of the Hudson River in Riverside Park.
Detectives originally suspected they had jumped from the George Washington Bridge, but changed their theory due to a lack of physical injuries they would have suffered in such a fall.
Instead, they now believe the girls walked into the water alive with their waists and ankles loosely bound with duct-tape, and that no crime was committed against them that caused their deaths.
According to the Chief Shea, an eyewitness came forward on Wednesday because of a "story that is haunting him".
The man said that he was exercising in Riverside Park when he saw two people believed to be the sisters sitting about 30ft (9m) apart near the waterfront.
"They were sitting with their hands in their heads," Chief Shea said. "Their heads lowered and they were making noises loudly that he described as praying."
Police say the sisters arrived in New York City on 1 September and "maxed out" their credit cards by ordering meals, shopping and staying at upscale hotels.
They add that their money was beginning to run out at the time of their deaths.
The siblings had moved to Virginia with their mother in 2015, and the older sister had been enrolled in George Mason University until this past spring.
They were reported missing and placed in a shelter after they were located due to abuse allegations.
But at the end of August, they again vanished before their bodies were found in New York.
Police are still appealing for anyone who had met the sisters since August to come forward with further information.