What court I need to file paperwork in order to amend my husband's death certificate after his live in girlfriend amended it once?

He was living with another woman at the time of his death in the state of NJ. She put herself on his death certificate as his wife. I am trying to get the death certificate amended. She already amended it because she must have found out that what she did was illegal. I send all my documentation to the Vital Statistics Office and they informed me that I need to go to court to amend it. I want to get widow benefits and his social security. Also, I have been getting the run around because no one seems to be able to tell me what court I need to reach out to get the paperwork that I need to file. I have called around from one office to another in the county he resided as well as my own county. I don't want to hire an attorney for something that should be simple enough for me to do on my own. Please help!