“My question is How should we file, Married head of household filing separately for both , I just dont know. “---->If you file MFJ on your federal return, you have to file that way for NJ. However, you only have to pay taxes on NJ-based income, so it works out in YOUR favor; your spouse, as nonresident of Montana( I mean UNLESS Montana is her home state) needs to pay her state income tax on the income that she earned in Montana (Unless no reciprocity agreement between NJ and Montana) to Monta and can claim state tax return on her NJ tax return( if either NJ tax rate is higher than that of Montana or general sales taxes that you paid are higher than either Montana or NJ state taxes). if your spouse’s principal abode is Montana (meaning that's her principal home, and she spends less than 183 days in NJ), then you can file in NJ as Married Filing Separate even though you are are filing your federal return as Married Filing Jointly. She reports her full income to Montana and pays tax accordingly. Your income is not reported to Montana, as you are a non-resident of Montana with no Montana-based income. In this case, your spouse DOESN’T NEED to pay tax to NJ, either as she is not a full resident of NJ and no NJ source income. To qualify for head of household status, you must be either unmarried or considered unmarried on the last day of the year. You are considered unmarried on the last day of the tax year if your spouse did not live in your home during the last 6 months of the tax year. Your spouse is considered to live in your home even if he or she is temporarily absent due to special circumstances, you paid more than half the cost of keeping up your home for the tax year, You file a separate return( both federal and state returns), Your home was the main home of your child, stepchild or qualifying person. Head-of-household filing status allows a taxpayer to choose the standard deduction, even if the taxpayer's spouse chooses to itemize deductions. If you, as a married individual, file a separate return with head-of-household status and elect to itemize deductions on your Sch A of 1040, and if your spouse continues to file as married filing separately, then your spouse is not eligible for the full standard deduction. Also, if your spouse who files separately elects to itemize deductions, then you who files a separate return with head-of-household status may still use the full standard deduction available for head-of-household status.
Please visit the IRS website for further info onhOH status here; Publication 501 (2010), Exemptions, Standard Deduction, and Filing Information