Yes, it may be possible:
Regarding New Jersey:
Each public school district sets up its own rules and boundaries for each school in the district, so it is best to check with your local district to find out which school your child will be assigned to, and what the rules are for attending charter schools, magnet schools, or other schools within or outside your local district.
Choosing a School in New Jersey - New Jersey - GreatSchools.net
If you have any further questions, please let me know.
Peace, Love & Happiness,
The Mystic Wave