In the first incident, authorities are searching for the young vandals who damaged a synagogue in the middle of the afternoon.
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The NYPD says video footage shows two people throwing a milk crate and a metal mailbox at a temple in Williamsburg.
They were with at least three other people outside the Throop Avenue synagogue.
The impact broke a window.
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Governor Andrew Cuomo directed the State Hate Crimes Task Force to investigate, issuing the following statement:
"I am disgusted and enraged by yet another anti-Semitic act of vandalism, the desecration of a synagogue in Williamsburg over Rosh Hashanah, one of the holiest days in the Jewish calendar. It is simply unconscionable.
"I am directing the New York State Police Hate Crimes Task Force to offer assistance to the NYPD as they investigate this disturbing act. This incident unfortunately underscores the need for State Police to increase their patrols around houses of worship during the Jewish high holidays this year.
"In New York we have no tolerance for hate and I continue to join with our Jewish community and work to ensure the New Year is one of peace, protection and well-being."
Mayor Bill de Blasio also condemned the crime on Twitter.
In a separate incident on the same day, a Jewish woman was allegedly targeted while walking in Bedford-Stuyvesant with her children.
Surveillance videos captured someone ripping off her headscarf and wig.
Jewish woman attacked, wig removed in Brooklyn
Anyone with information in regards to this incident is asked to call the NYPD's Crime Stoppers Hotline at 1-800-577-TIPS (8477) or for Spanish, 1-888-57-PISTA (74782).
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