Are we talking about shoplifting? Because like I said earlier, once you leave the property there's nothing they can do. Unless they have video of you taking something from the store. Of course they also need your name and address but that's something else.
In New Jersey you cannot be arrested on an employee's word if there's nothing in your possession. We're not talking about rape or assault here. That's a different story but shoplifting is different. The items you are accused of taking have to be found in your possession (unless they have video).
That's not shoplifting, at least in my state. That's obtaining property under false pretense, a felony.