It happened at Holy Cross Church on Tuesday afternoon.
The suspect tried to push over two statues before finally pushing over the Our Lady of Fatima statue and destroying it after it broke into several heavy pieces.
The pastor there does not believe it can be repaired and the congregation is very upset.
Surveillance video from nearby offices captured the suspect on camera.
Police hope the public can help to identify him.
Anyone with information is asked to contact the Harrison Police Detective Bureau at (973) 483-5101.
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