The tax reciprocity for DC only applies if you retained your residency in the other state while working in DC.
If you did not retain your other state residency while working in DC for the congressional committee, and actually lived in the District, you will need to file a Part Year Resident tax return for both DC and Louisiana.
For more information, follow these links:
DC
Special Circumstances
http://revenue.louisiana.gov/IndividualIncomeTax#nriit