Yes, you should enter the form W2 information however, generally NJ does not tax "Third party sick pay." Amounts received by an employee through an accident or health insurance plan for personal injuries or sickness are not subject to income tax in New Jersey. Here is a NJ reference.
Check/enter form W2 as follows (extracted from the Learn More link in the NJ state interview after entering a W2 for sick pay.)
"The state portion of the sick pay W-2 should be entered as follows:
In Box 15 enter "NJ" ,
If the "Employer State ID No." box has a number, enter it from the W-2, if not enter the federal ID number without blanks or dashes.
If Box 16 is blank or 0, enter "0",
If Box 16 has an amount greater than "0", verify that the amount does not include third-party sick pay. If you feel there is an error, you may need to talk to your payroll provider.
If Box 17 is blank or 0, enter "0"
"For these "third-party sick pay" W-2s, Box 16 should tell you how much of that W-2's wages are taxable in New Jersey. In other words, your New Jersey third-party sick pay should already be taken out of Box 16.
If all the wages on your W-2 are third-party sick pay, then box 16 will generally be "0" or blank.
Important: If you have "NJ" in Box 15 of your W-2 and the corresponding Box 16 (state wages) is blank, enter "0" in Box 16. Leaving it blank may result in the Box 1 wages being treated as taxable in New Jersey.
Sometimes, your "third-party sick pay" W-2 will have an amount in Box 16 other than zero. This amount is generally taxable in New Jersey. Often, this is the amount of wages your employer paid in the "initial" period of your absence - before a third party took over payment of the sick pay benefits."
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