File two part-year returns for Maryland and New Jersey and report on each return what income was received while you were living in each state.
If you were a part-year resident of New Jersey, you can’t claim yourself as a full-year MD resident and a NJ nonresident.
Maryland does tax unemployment, so any unemployment received while you lived in MD is taxed by MD. States give you a credit on double-taxed income, but because NJ does not tax unemployment, there is no credit.
The income is not reportable to NJ, but reportable and taxed by MD.
Property tax deduction/credit
New Jersey has a property tax deduction/credit. If you have no NJ income, you may qualify for the property tax credit of $50.
NJ Income Tax Property Tax Deduction/Credit for Homeowners and Tenants
Homestead benefit
If you were a NJ resident on October 1, you would qualify for the Homestead Benefit. The benefit is normally a credit on your local tax bill, but a nonresident can get check.
The Homestead Benefit is paid several years later (NJ is up to 2018), but filing a return will get your info into the system.
Homestead Benefit Program
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