It's kind of a quirk in New Jersey law. There was an orthodox Jewish boy hooked up to a respirator and his parents didn't want to let him go. New Jersey has that exception, so they may not be tied to a California death certificate, although the Full Faith and Credit Clause could be invoked since a determination of death is considered a public act.
Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.