The S corporation must qualify to do business in NJ. The forms are available on the New Jersey Secretary of State's web site. It may also be required to obtain a NJ contractor's license; check with the NJ Department of Consumer Affairs.
A corporation is subject to the New Jersey corporation business tax if it is doing business in NJ, deriving income from sources in NJ, or "engaging in contacts in New Jersey," among other things (N.J. Admin. Code 18:7-1.6). If the S corporation is acting as the general contractor on a project in New Jersey it will surely be doing all of those things. The form to register for the corporation business tax is available on the Department of Revenue's web site. Also, in order to be treated as an S corporation for NJ tax purposes, the corporation must file a NJ S election; without it, the default is to C corporation treatment. (This is similar to NY.)
Each of the stockholders will be an individual income taxpayer in New Jersey on the flowthrough income apportioned to New Jersey. Stockholders who are nonresidents of New Jersey must consent to jurisdiction to tax their NJ source income; the corporation must withhold and pay over tax on the distributive shares of any nonconsenting nonresident stockholders.
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