Is it Obstruction of Justice if I don’t provide ID to a police officer in a non stop and ID state?

I was walking to my car in a shop rite parking lot when I was approached by an officer , long story short they received a call about someone pulling door handles and said I matched the description, when he asked me for my if so he can “write down who he is talking to” I politely refused as New Jersey is not a Stop and ID state and I know I have not committed any crimes. The officer then threatened to arrest me for obstruction , I know he technically is allowed to say what he wants but could he actually charge me with obstruction?