Where to assign income that my W-2 says was earned in DC?

Here's the situation, pretty straightforward:

* I was hired by the federal government in 2019. At the time, I was living in State A. * During my training, they entered "Washington, DC" as my duty station (even though training was actually elsewhere). Because I was still domiciled in State A, I had payroll change my withholding back to State A. * After training, I was assigned to State B, and my withholding changed to State B.

All good so far. I'll file part-year resident returns in both State A and State B, no problem. Because I wasn't able to talk to payroll immediately, I did have some taxes withheld for DC; I know I can get them back by filing form [D-40B](https://otr.cfo.dc.gov/sites/default/files/dc/sites/otr/publication/attachments/2019%20D-40B_0002.pdf).

My question now is: what do I do with the income that was assigned to DC? Really it should have been assigned to State A, but my W-2 lists all three (DC, State A, State B). If I get the withheld tax back from DC, now I have some money that I owe State A.