In NY State notary public cannot perform copy certifications of any document - neither publicly recorded nor private.

If you need a certified copy of any of publicly recorded documents like:

• Birth, marriage, and death certificates; 
• Certificates of citizenship or naturalization; 
• Documents filed in a court proceeding; 
• any form of ID (passport, driver license);
• Documents recorded by the Clerk of the Court; 
• Public records maintained in government offices; 
• Student records (transcripts, etc.) kept in public education offices; 
• Already filed federal or state income tax forms; 

- you  may only obtain it from the custodian of records. 

In case of NYC vital records such as birth certificates, marriage certificates or death certificates - certified copies would have to be obtained from the NYC Health Department (birth and death records) or the NYC Marriage Bureau (marriage records).