According to Section 302 of the Veterans Benefits and Transitions Act (VBTA) of 2018, the spouse of an active duty Servicemember can elect to have the same residence for state and local tax purposes as the
Servicemember. In other words, if a Servicemember is a legal resident of a particular state for tax purposes, the spouse can unilaterally elect to also be a resident of that same state, even if he/she has never lived there. The law went into effect starting with tax year 2018.
https://www.congress.gov/bill/115th-congress/senate-bill/2248/text
Therefore, for state tax purposes your wife may elect to be a resident of your SLR of New Hampshire, thus relieving her of the obligation to file a tax return in either MA or MD.
She should file Form M-4-MS with her Massachusetts employer, certifying that she is exempt from MA withholding: https://www.mass.gov/doc/form-m-4-ms-annual-withholding-tax-exemption-certificate-for-nonresident-mi...
The similar form for Maryland is MW507M: https://www.marylandtaxes.gov/forms/20_forms/MW507M.pdf
In order to obtain a refund of the withheld MA taxes, she must file a non-resident MA tax return, showing zero MA income. The return should be printed and mailed, because of the likelihood that an e-filed return will be rejected because of the W-2 discrepancy.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
