The National Weather Service was reporting 3 1/2 inches in Whitehouse Station, nearly 3 inches in Ewing, 2 inches in Somerville and an inch in Brick Township.
Snowfall amounts could be higher in Mercer, Salem, Gloucester, Camden and northwest Burlington counties.
By Tuesday morning, New Jersey State Police troopers had responded to more than 80 accidents throughout the state.
There's a 45 mph speed restriction on the New Jersey Turnpike in both directions from the George Washington Bridge to the Delaware Memorial bridge.
The speed limit has been lowered to 45 mph on the Garden State Parkway from Hazlet to Cape May and 35 mph from Hazlet to the New York state line.
NJ Transit will offer systemwide cross-honoring through the end of the service day Tuesday due to the storm.
The federal courthouses in Newark, Camden and Trenton are closed because of the weather.
The new storm comes on the heels of Sunday's snow that brought several inches to parts of the state.
"Three inches isn't so bad, doesn't get in the way too much," said Volkert Veeder, a Toms River resident.
Volkert Veeder almost hit the mark. Toms River is expected to get two to four inches of snow Tuesday. Homeowners are geared up, but not quite preparing for snowmageddon.
"I've got a good neighbor with a snow blower," Veeder said.
But the town doesn't want to get caught off guard, an unexpected eight inches of snowfall led to dozens of accidents and 911 calls from upset residents.
"I think this took people by surprise," said Chief Michael Mastronardy, of the Toms River Police Department.
Dozens of schools statewide have closed due to the storm.