Sandyston in Sussex county recorded -32 in the January 1994 cold outbreak and is probably more legitimate although they do recognize that -34 in River Vale in 1904.
I'm about 45 miles east, northeast of Sandyston in Orange County NY, Highland Mills, and I recorded -23 that morning. There were numerous readings below -20 county wide in Orange and NW jersey so it's not far fetched a sheltered valley hit -32. Plus the snow cover was pretty deep area wide at that time.