I live in MD - work in DC - Employer did not withhold states taxes from either state. What do I do?

You will need to pay taxes in Maryland.  And in the future, make sure your employer withholds your state taxes. 

Since DC and MD have a tax reciprocity agreement, you do not owe DC taxes. 

For more information, follow these links:

Intuit on Tax Reciprocity

MD Tax Reciprocity