Vital Records Services - New York State Department of Health
www.health.state.ny.us/nysdoh/consumer/vr.htm#application 

New York City maintains its records separately from New York State, and within NYC there are three agencies with vital records:

NYC Municipal Archives 
www.nyc.gov/html/doris/html/1vital.html 
(older birth, marriage and death records)

NYC Dept. of Health and Mental Hygiene
www.nyc.gov/html/doh/html/vr/vr.html 
(more recent birth and death records)

City Clerk's Office, Marriage License Bureau
(more recent marriage records)
www.nyc.gov/html/doris/html/cityclerk.html