The incident involved graffiti and vandalism to the cross, which can usually be seen from Honness Mountain in the area of Brooks Road in Fishkill for miles, including from Route 9 to the west and I-84 to the south.
New York State Police from the Wappinger barracks said the investigation is being conducted with its Bias Crime Unit.
In a post on Facebook, James Brooks said his grandfather "thanked God every day for his son (my father) living through a fire that burned a major percentage of his body.
"So he built a cross on the top of our property to thank God for sparing his son."
Brooks said the cross has been destroyed three times in two years.
In the latest incident, on Thursday, Jan. 2, the vandals cut the four cables that restrain the cross from moving before getting below the ledge and using either a rope or other device to bend it, Brooks said.
"I'm tired of it," Brooks said. "Anyone who gives information leading to an arrest gets a reward. Let's start at $500. ... Please spread the word."
Anyone with information is asked to contact State Police investigators at (845) 677-7300.
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