You don't have to do anything.
Here's the link to Home School Legal Defense Association's "Legal Analysis of New Jersey Law":
http://www.hslda.org/laws/analysis/New_Jersey.pdf
I'm not going to advise you about whether you should call the school or not, but if you do, or if the school calls you back, all you need to do is say that you're going to homeschool. You don't need anyone's permission, you don't need to fill out anything; usually you don't even need to notify anyone, but since you've already had some contact with the local public school you might need to have a brief conversation just so no one thinks your dc is truant.