From the description of this 1930 headstone report it doesn't sound like it's attached to a church. I have ancestors from there, but do not live there. Maybe someone from Sullivan County, NY could answer your question better than what the link below says. http://dunhamwilcox.net/ny/sullivan_cem13.htm
"WHITE SULPHUR SPRINGS CEMETERY, White Sulphur Springs, Sullivan County, New York, in the rear of the Hotel (next to Post Office, on main street. In fair condition."