Is This A Fireable Offense And If So How Do I Go About It For Someone At A Government Job? (new York State)

My grandma lives in a government owned elderly facility. The front desk security guard has been very rude to my family ever since my grandma recieved a very bad medical diagnosis. We take turns coming in and taking care of her and come often. Recently she was very rude to us and I said "there's no need to be so ugly to us all the time". Her response was she yelled "You think your grandma is so special don't you. Get out of here f*gg*t". I responded "nice to know you're a homophobe too" and she yelled "I'll beat your ass. Die you fucking f*gg*t" at me even after I left the building. She left her post and she screamed it repeatedly the entire time I walked towards my car. How do I report this without it leading to nothing but her making life for my grandmother even harder.
Edit: censoring the slur
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