Tala and Rotana Farea, the sisters from Saudi Arabia whose bodies were found taped together in New York City's Hudson River last week, were said to have preferred suicide over returning to their home country, according to police.

Dermot Shea, chief of detectives for the New York City Police Department, said "sources" in Virginia, where the Farea sisters had previously been living, informed investigators that the two women had been in the United States for two to three years and would "rather inflict harm on themselves and commit suicide than return to Saudi Arabia."

"Everything that we’ve seen thus far is pointing to something other than a crime taking place," Shea told reporters at a news conference Friday afternoon. "But we’re not ruling anything out."

Detectives believe the women may have applied for asylum in the United States after alleging that they were victims of abuse, Shea said.

The medical examiner's office will ultimately determine the causes of death as the investigation continues.

A witness told police he saw the women in a park on West 158th Street in Upper Manhattan on the morning of Oct. 24, while he was out exercising. They were sitting about 30 feet apart with their heads in their hands and appeared to be praying, the witness said.

The bodies of Tala Farea, 16, and Rotana Farea, 22, were seen floating along the Hudson River that afternoon, police said.

The sisters, whose bodies were loosely bound together with duct tape, were found lying on rocks near the river, fully-clothed, both wearing black jackets with fur trim and black leggings. There were no obvious signs of trauma, and detectives believe the women were alive when they entered the water, according to police.

Their bodies are believed to have washed ashore with the tide and stayed when it went out, police said.

NYPD detectives are checking to see if any surveillance cameras captured the moment Tala and Rotana Farea entered the river. They are also trying to determine whether either of them had met with any counselors or therapists in recent weeks, two police sources told ABC News. (ABC News)

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