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. 

We are going to  file jointly in NY. She also worked in NY at the beginning of the year.

I am not clear on the implications or advisability of filing both a joint New York nonresident return at a joint New Jersey resident return. You may want to have a professional review. In any case, your wife’s HSA contributions will be excluded from her taxable income on her federal return and they will be added back to her income on the New Jersey return.

If any of her HSA contributions through payroll deduction can be allocated to the period of time when she was working in New York, they will already be excluded from her wages. You can’t take an additional deduction.  If she made separate additional contributions from out-of-pocket funds which are separately deductible on the federal tax return, they would be allocated to New York if the contributions were made during the time she was working in New York.

Thank you.

In 2021 I'll be the only one working in NY. Should I file married filing separately? What's the advantage to that, aren't the tax rates better for filing jointly?