Police investigated the reports of possible vandalism at Washington Cemetery, a Jewish burial ground.
Investigators said the damage was likely caused by maintenance and environmental factors (wind), and the cemetery operators concurred with the findings of the detectives.
New York State Assemblyman Dov Hikind tweeted photos of the gravestones.
In a statement on Sunday, Hikind said he is still skeptical that wind was a factor in the damaged gravestones. Hikind said in part, "So strong winds hit this section and left the other ones alone? I find that hard to believe. Something is definitely not kosher."
Hikind said he was alerted Saturday night about the situation, saying more than 40 headstones were overturned, and was immediately in touch with the police to make certain that the matter was being investigated.
The NYPD says after consultation with with cemetery management, it was determined the 42 tombstones came down as a result of a number of factors.
Those include long-term neglect or lack of maintenance, as well as environmental factors such as soil erosion.
An NYPD spokesman said the department's hate crimes division was notified when the headstones were found toppled over.
There has been a wave of anti-Semitic incidents across the country, including other cemetery desecration in St. Louis and Philadelphia.
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(The Associated Press contributed to this report.)