Vital records such as birth, marriage, and death certificates are not handled by the County Clerk. Instead those are handled by the city, town or village offices where the event took place.
Alternately you can order certified copies of birth, death, marriage & divorce certificates by using VitalChek or the direct link for NY State Vital Records.
In the event that visiting your hometown isn't possible, you may obtain a Birth Certificate directly from the New York State Department of Health at www.health.state.ny.us/vital_records/birth.htm or by calling 1.877.854.4481.
For Pennsylvania birth records please apply through the Pennsylvania Department of Health, Division of Vital Records at www.health.pa.gov/MyRecords/Certificates/Pages/11596.aspx#.VS_zXhczMkV.