Expenses paid through an HSA are never deductible, if have already received the tax benefit of the HSA contribution. The HSA contribution will show in box 12 of your W-2 with code W. This will then populate to your state return. These contributions are reducing the income reported in box 1 of your W-2, thereby reducing your taxable income for the state, if it is allowed in your state.
The contributions will be reducing your NY income, as it was NY-sourced income. Employer contributions to HSAs are included in NJ income and employee contributions are not deductible on the NJ individual tax return.
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