Contact the town where the individual was born to see if the municipality can provide a copy.  Otherwise, contact the State of New Jersey's Department of Health and Senior Services.  

Look up Contacts for the 21 municipalities in Somerset County.  If the individual was born at Somerset Medical Center in Somerville, call the Somerville Department of Health and Vital Statistics at (908) 725-2300, ext. 1980 or 1982.

New Jersey Dept. of Health and Senior Services – Vital Records

120 South Stockton St.
Trenton NJ 08625
Phone: (609) 292-4087

Vital Records in New Jersey