You must file in FEDERAL court, as bankruptcy is Federal law.
Each state is divided into districts. NY is, not surprisingly, divided into 4 N,S,E, & W.
Broome County is part of the NY Northern District, usually assigned to Utica courts, 341 meeting usually held in Binghamton.
Here's a list of the counties covered:
http://www.nynb.uscourts.gov/usbc/welcome/32CTY.html
This is the Northern District's web site:
http://www.nynb.uscourts.gov/
Make sure you pay close attention to the Local Rules for filing.