Officers were called to Washington Cemetery on Saturday evening and ordered an investigation to determine whether or not the incident was a hate crime, police said.
"Upon further investigation... it appears that the tombstones were toppled as a result of either long-term neglect, lack of maintenance or environmental factors," a spokesman later told AFP.
Recent weeks have seen scores of bomb threats against US Jewish organizations and at least three other Jewish cemeteries desecrated.
Some critics have blamed President Donald Trump's sometimes incendiary rhetoric and policies, which they say have stoked feelings of insularity and xenophobia.
Last month, New York State Governor Andrew Cuomo promised a $25 million grant to boost security and a $5,000 reward for information leading to arrests and convictions for hate crimes.