The answer is yes. New Jersey is one of five states that treats a telecommuter working from a home office in behalf of a New Jersey company to be working in New Jersey. (They use a principle called the "convenience of the employer" to do so). Since you were living in NH for at least part of the year while working for the NJ company, you will answer yes to the question if you earned income in NJ while living in another state. (You will be taxed in NJ as a nonresident on that portion of your income).
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