It should be his agency I.D with the words "retired" on it. If I'm not mistaken. So your Dad's case it should say "NJ Police retired" with his name and etc. Badges aren't 100% acceptable in terms of demonstrating a status of a peace officer. He'd also have to take LEOSA training and obtain a permit.
Read more here on the states website:
Just to clarify I'm not a Peace Officer, I'm a Security Professional who has somewhat of a knowledge of this stuff. I'm sure somebody else could better explain it.