Tala Farea, 16, left, was found dead with her sister Rotana Farea, 22, in New York City on October 24, 2018.
It continued that it is not clear how Tala, 16, and Rotana, 22, died, but said there was no information to suggest foul play.
One theory had been that the sisters had jumped from the George Washington Bridge, but that was ruled out after the medical examiners' office said there were no obvious signs of trauma on the bodies.
The sisters moved from Saudi Arabia to Fairfax, Virginia in 2015 with their mother, and had a history of running away from home, according to USA officials.
Police sources told the New York Daily News the pair had been bound together and their sandals duct-taped to their feet.
"At this point in time it has still has not been determined a homicide", NYPD Chief of Detectives Dermot Shea said, adding that he and his department are on a mission to find out what happened.
As indicated by the Arab News, an English paper in Saudi Arabia, their mom revealed Tala, the younger sister, was reported missing months ago but called off the search once she found out that Tala was staying with Rotana in New York City.
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Saudi Arabia's consulate general in NY did not comment on the Times report directly.
The Saudi embassy in Washington said yesterday that it was extending its "support and aid in this trying time" to the family.
"We are looking at all clues in their past life", Shea was quoted as saying.
Still, the NYPD is not ready to officially determine the causes of death.
Rotana was enrolled at George Mason University, but left in the spring. Police are investigating the possibilities of a suicide, but they're not ruling out murder.
"They were a democratic family, they never had any issues and the eldest was sent to college in New York City with her family's blessing", they said.
Their families claimed the sisters had been missing since August 24 after leaving the shelter in Fairfax.
Police said the sisters left their family home and were placed in a shelter after an earlier disappearance in December 2017.