Yes it is possible you may owe both states. Each state has their own tax brackets/rates/taxable income/deductions/credits, etc. For NY as your non-resident state You will only pay NY taxes on whatever income is taxable by NY. If the NY withholding and NY credits was not enough to cover the NY taxes then you will owe there.
When you enter your form W2 that has NY income and withholding showing in boxes 15-17 then the withheld amount is credited on your NY return. In the NY interview you have the opportunity to allocate only the income that belongs to NY to NY. Be sure to zero "0" any income sources that are not NY sources. Complete your NY non-resident interview first and take note of the income taxed and the tax liability in NY. TurboTax will transfer that information to your resident MD return to claim a credit there; it is not always dollar for dollar.
Generally the same will be true with MD, with one difference. MD is your resident state and your resident state taxes income no matter where it is earned; there is no allocation. There is however an opportunity to claim a credit for taxes paid to another state (NY) on your resident return. In the MD interview, in the credits section you will have the opportunity to claim that credit.
Again if your MD withholding and MD credits are not enough to cover your tax liability for your MD taxable income you will owe.
For live tax advice click the box "Live Tax Advice" in the upper right hand of your online TurboTax screen and follow the prompts.
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