Is water company responsible to fix water leak at curb in New Jersey ?

It goes by town ordinance. 'At the curb' can get contentious, because you may own the land at the curb, they may own it, or you may own it but they maintain sidewalks and curbs.
Have you asked the town yet?
Has anyone dug up the street yet to locate the street valve?
I claim that if the valve there is defective, they should replace it.
Be sure to take pictures and write down everything that happens, who you talk to, and when.
Be nice at first. Then pound on desks!
And you may have to haggle over your next water bill too.

Some location it is at the main pipe, some at the valve, some at other places. Ask you local water district, they are all different.

The issue is "at the curb" where in the pipe, is the water leak. Is it the valve, is it before or after the valve.

In every city I have lived in, if it is the value or before the value, the city or water company fixes. If it is after, the homeowner fixes. But I understand some areas have different rules.

In my area, Water Co. is responsible for pipe up to the meter + the meter. After the meter, water leaks are homeowner's responsibility.

Milo

In my experience in NJ (with Southeast Morris County Municipal Utility Association) the water company does repairs up to the shut-off valve, which ought to be located on your property near the curb. Any leaks between the shut-off valve and the water meter in the house are the home owner's responsibility.

I agree with the last two, meter on out to the street belongs to the water company.

I would imagine the first step is to call the water company and if it's their problem they will fix it. If it's yours, I am very positive they will tell you, but you have to call them to identify the problem, and go from there.