Maybe. If you are a US citizen or long time permanent resident, some states tax you while you live abroad until you establish residency in another US state.
Some states are more aggressive than others about this.
You must file a DC resident return if-
• You were a District of Columbia (DC) resident in 2016 and were required to file a federal income tax return. (A resident is an individual whose permanent legal residence is within the District during the taxable year); or
• You maintained a place of residence in DC for a total of 183 days or more during 2016 even if your permanent residence was outside DC (see instructions for part-year residents, page 25)
DC doesn't provide too much information on living abroad. However, if your permanent legal residence is DC and your stay abroad is only temporary, ALL of your income is taxed by DC, including your UK income. If DC is your legal home state, it gets to tax your worldwide income just as the federal government does.
Have you established residency in the UK, or are you simply working there right now? The facts and circumstances of your situation matter.
http://otr.cfo.dc.gov/page/individual-income-tax-filing-faqs
