Early vital records in New York were recorded & filed in the Town Clerk's office. You can contact the Hillsdale Town Clerk, http://hillsdaleny.com/town-clerk/about-town-clerk/
However if she was adopted, you might have to look elsewhere for her birth record. The Columbia County Historian, 518-828-3442, might be able to help you with where to find early adoption records. Successful Searching!