N.J. Stat. § 23:4-25
The owner, lessee or custodian of a dog found running at large in the woods or fields, shall be liable to a penalty of $20.00 for each offense; provided, however, that the occupant of a farm may permit his dog to run at large on the land he occupies, except during the open season for deer.
The owner, lessee or custodian of a dog may go into the woods or fields with the dog without firearms for the purpose of exercising or training it in daylight at any time, except during the open season for deer, provided that on State public shooting and fishing grounds or wildlife management areas such exercising or training may be restricted to designated areas, and raccoon dogs may be trained between the hours of sunset and sunrise for a period of 4 weeks prior to the last week preceding the opening of the raccoon season unless prescribed otherwise by the Fish and Game Code. The penalty for violation of this section shall be $20.00 for each offense.
Any person going into the woods or fields with a firearm, except during the open seasons for the taking of birds and animals as prescribed by law or by the Fish and Game Code, shall be liable to a penalty of $20.00 for each offense; provided, however, that this section shall not apply to the killing of crows, yellow-headed redwinged, bi-colored redwinged, tri-colored redwinged, Rusty and Brewer's blackbirds, cowbirds, grackles, woodchuck and vermin other than birds, which may be taken in any manner and at any time of the year, when in the act of destroying poultry, crops or property.
N.J.S. § 23:4-25