Yes, on the New Jersey return, TurboTax will automatically add the "employer contribution" to your HSA (this is the code W amount in box 12 on your W-2) to your Wages in line 15 of the NJ-1040.
You need to check with your HR or payroll department, because normally those people add these pre-tax items like HSA contributions back to state income when your W-2 is printed - but it is good to confirm.
On the federal return, the employer removes HSA contributions made through the employer from Wages in boxes 1, 3, and 5 on the W-2 when it is printed. Since New Jersey does not allow the deduction of HSA contributions, this is why the contributions are added back to state income.
Still, the only way to be sure is to ask your employer.
[Edited 3/23/2020 11:34 am CDT - changed intro]
