First, define what kind of hat it is - top hat, derby, straw boater? This will help refine your search.
The Hat Museum in Portland Oregon displays many old hats. You can learn a lot from their website.
Genin had a huge business in New York owning one store near the corner of Ann and Broadway, and another department type store. His specialty was theatrical costume design.
A free online book may help you. "Hatatorium An Essential Guide for Hat Collectors" by Branda Grantland, Mary Robak, etc. (2013). Also, check out "Antique Trader Vintage Clothing Price Guide" edited by Kyle Husfloen and Madeline Kirsh.