It all depends on where you lived and where you worked during the year.
Scenario 1: You lived in DE but worked in MD: In this case, you would pay state taxes to MD on the income you earned there.. You should have filed a non-resident MD return and on your resident DE return, you should have received a credit for the taxes that you paid to MD.
Scenario 2: : You lived in MD but worked in DE: In this case, you would pay state taxes to DE on the income you earned there. You should have filed a non-resident DE return and on your resident MD return, you should have received a credit for the taxes that you paid to DE.
You may need to amend your MD & DE tax returns if they were not prepared using the guidelines above.
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