Unfortunately, yes, you need to file in both states. You file in MD because you are a resident and all income earned while you are a resident, irrespective of where in the world it came from, is taxable by MD. You file in DE because you earned income from DE sources. Fortunately, MD allows a credit against its tax bill for income taxes paid to DE.
The Maryland site (http://taxes.marylandtaxes.com/Individual_Taxes/Individual_Tax_Types/Income_Tax/Filing_Information/D...) states:
If you work in Delaware
Maryland residents who work in Delaware must file tax returns with
both states. To avoid dual taxation, you can get a credit for taxes paid
to Delaware and/or a locality in Delaware by completing Maryland Form 502CR
and filing it with your Maryland income tax return. Be sure to include a
copy of your Delaware return and/or return of the locality in Delaware.
Yes
No
