Per the State of New Jersey, you would not have to file a part-year return for your level of New Jersey sourced income (approximately $2,000 as you stated above). Therefore, if you do not have to file a return, you don't have to claim an exemption on the coverage. Even if you did file, you would not have to pay a penalty due to your income level, as WendyN2 stated previously.
That being said, if New Jersey taxes were withheld from your income, then you should file to get a refund of tax paid.
For NJ filing information and limits on income, please see NJ-1040NR.
@drsalmanshah165
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