It's taxable.
I asked that question at the New Jersey Division of Taxation web site. It took 2-1/2 months to get an answer, but here it is.
Question
The instructions say Scholarships are not taxable if the primary purpose of the grant is "to further the recipient's education or training." Room and board are not "qualified expenses" on the federal return. Are scholarships that pay for room and board taxable on the NJ return or does room & board expenses meet the definition of "to further the recipient's education or training"?
Answer
"A qualified scholarship is fully exempt from New Jersey Gross Income Tax and withholdings under N.J.S.A. 54A: 6-8. Generally, tuition, fees, books, supplies and equipment are excluded for New Jersey purposes.
However, additional compensation (amounts for general living expenses such as room, board, travel, etc.) paid in excess of tuition and the related expenses as mentioned above are included in income and not tax exempt."
