Yes. A Building Permit is required for any fence going around a swimming pool, spa, or hot tub. The fence must comply with Appendix G (PDF) of the 2006 International Residential Code NJ edition. You can pick up a permit package from the Building Department at 357 S. Livingston Avenue, 2nd floor, or online here.
A Zoning Permit is required for any fence on your property other those listed above. You must comply with Fence Ordinance (PDF) and file for a Residential Zoning Permit (PDF). For more information, please call Cathy Jackson in the Zoning Department at 973-992-1595.