The NY City Municipal Archives has released a new website that will contain free copies of birth, marriage, and death records that are in their collection. The website is here -
https://a860-historicalvitalrecords.nyc.gov/?fbclid=IwAR2QHeKfcEQb1Dc2A1oJeo04knt3z-D76-1pR6KSKcGJSd3gPbysnjLIrbA It seems the site is currently overloaded or not working properly and that all available records have not yet been indexed, but this should be a very helpful resource in the future. The time frames that should be covered are:
Birth records, 1847-1849, 1853-1912
Marriage records, 1829-1949
Death records, 1795, 1802-1804, 1812-1948