Unemployment benefits are not taxable in New Jersey so a return does not have to be filed there. The filing threshold is $20,000 ($10,000 for married filing separately), but since you will subtract all of the unemployment benefits your income will be zero for New Jersey which will result in zero tax.
Maintain your records should you be questioned at a later date, which is not likely since this is your only income.
For more information you can use this link: NJ Unemployment
Benefits
