No.   You are not eligible to receive a certified copy. However, you can have the life insurance company request it directly from the State Bureau of Vital Statistics and Registration. The request must be made on their agency letter head and list the name and social security number of the deceased. They must also provide Acceptable Forms of Identification and the appropriate  Fees.  
In many cases, the insurance company will provide a letter indicating they are in need of the death certificate and require you to submit the application for the certified copy of the record, which you must identify. In this case, you must include the insurance company letter in your application and the resulting certified copy will be mailed directly to the insurance company.

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Mailing Address:
Post Office Box 728,
Toms River, New Jersey 08754-0728
Town Hall located at:
33 Washington Street
Toms River, New Jersey 08753
732-341-1000