Enter the NJ tax withheld in the federal return so that the withholding can be included in your federal itemized deductions. TT/New Jersey will pick it up from there.
Federal Taxes tab (this is the Deluxe version path. Premier is similar)
Deductions and Credits
I'll choose what I work on
Scroll down to Estimates and Other Taxes Paid
Select Other Income Taxes
Under Other Income Taxes Paid in 2018 is
Withholding not already entered on a W-2 or 1099 <Start>
Enter the $$ withheld in the State box and select New Jersey from the dropdown
Or, in Forms Mode, open Tax Payments and in line 18a (or b or c) enter NJ in the St box and the $$ in the State column.
