This number seems like it should work to get to the New Jersey unemployment office, but it doesn't. When calling it, I didn't get any kind of automated message or anything to suggest that I had reached the New Jersey Department of Labor. There was only a voicemail that said that the number I had dialed was not available.
I tried again and got the same message after about six or seven rings, as if I was calling a residential number. There was nothing to suggest that I was calling a government number and nothing to suggest this was an official number of any kind.
Upon searching for this number on the official New Jersey Department of Labor website, I didn't find it listed as one of the numbers needed to reach someone. There are four main numbers for reaching a live person, plus a number to reach the automated system, and this number doesn't come up for any of them. This number is similar to the automated system in that the first six numbers are the same, but it's a completely different number.
As I continued my search, I saw this phone number come up in the directory on the New Jersey Department of Labor's website. The website has an employee directory where you can enter in first and last names to search for someone, or you can enter in other identifying factors, such as their department or their phone number.
Strangely, when you enter this phone number, only one name comes up: a Gregory T. Castellani who works in the Labor Department. Other phone numbers listed in the directory are tied to multiple names, suggesting that those numbers simply go to that section of the New Jersey government, but this number only suggests that it goes to Gregory Castellani.
Given the lack of identification from this number and the difficulty of finding information about it online, it's difficult to tell if this number really does belong to the New Jersey Department of Labor's Gregory Castellani or if it's a mistaken number that isn't meant to be used for the unemployment department at all. The presence of the number on the directory suggests it's a genuine number, but actually calling the number suggests it's to Gregory Castellani's office line.
Obviously, given that this number didn't work and didn't provide any kind of identifying details to confirm what it does, I can't recommend using this number for customer service from the New Jersey Unemployment Office.