An HSA has only one owner. If your spouse contributes to an HSA, that is reflected on her tax return, not yours.
For your federal return, you probably file jointly. Your wife's HSA contributions are already reflected in her W-2 (they are excluded from box 1 taxable wages and are NOT a separate deduction, unless she also made additional out of pocket contributions.)
Then, for her NJ state tax return, the amount is added back to her wages because NJ does not recognize the deduction or exclusion for HSA contributions.
How do you file your state tax returns? Do you file separately or jointly? If you file a separate NY non-resident return, and a joint NJ resident return, your wife's HSA contributions have nothing to do with you and can't be included on your separate NY non-resident return. It's not your account and not your contributions.
