The New York State School for the Deaf, www.schoolandcollegelistings.com/US/Rome/12055479828
exists today and has been in busines for 140 years. They have an alumni association.
I don't know if they have their own archives or not. You might have to contact the Rome Historical Society, www.romehistoricalsociety.org/
to find more old history about the school. Successful Searching!