Typically what happens is when you file state taxes in two different jurisdictions, you will usually owe taxes in one jurisdiction and pay taxes in the other. Most of the time, the two amounts will offset each other.
DC and Virginia have a reciprocal state agreement whereas if you work in DC and live in any other state, no DC taxes will be withheld. To claim this exemption, you have to file form D-4A with your employer. Here is link to that form.
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