Judge Sheila Abdus-Salaam, 65, the first African-American woman on the New York Court of Appeals - the state's highest court - was found dead last month in the Hudson River.
On Wednesday, Chief of Detectives Robert Boyce said the New York Police Department had completed its investigation into her death.
He said investigators had tracked down all leads and found no criminality, and that her death likely was a suicide.
Evidence gathered by the police has been turned over to the city's medical examiner, who will make a final determination, Boyce said.
A previous autopsy was inconclusive.
When police found Abdus-Salaam's fully-clothed body in the river on April 12, there were no visible signs of trauma or foul play, law-enforcement officials said.
At the time, police said initial evidence indicated she probably had committed suicide.
But the judge's husband and other family members disputed the idea that she would take her own life.