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City Championships.
Lots of privates are in conferences with MD/VA schools. Though neither of those allow privates in state comp, these DC private schools often do have competitive conferences. WCAC for example. XC is admittedly more competitive in public but Catholics would clean up in many of the big sports. Which is probably why they aren't allowed...
Also, the DC HS system is tiny. There is 650K people total in DC. Just the 3 adjacent counties have 1M or more people each. DC publics would be uncompetitive and would virtually all be 1A in either VA or MD, if allowed.
technically yes they do, though i think everyone is aware there's no "state" of DC.
The DC state athletic assn. includes traditional public, public charter [i think about 50% of DC public school students are in charters], and private schools located in DC [someone mentioned WCAC, but that league covers VA, MD, DC].
Sometimes cities don't participate in state championships. Philadelphia never participated in the PIAA championships because it's city league was not part of the organization. I was in high school in PA when Simon Gratz was loaded with Rasheed Wallace and a few other Division I players and was ranked #1 in the country. They won the Philly Championship but were never the "state champion" even though it was well understood that nobody in the state could touch them on their worst day.
As a side note, Rasheed Wallace is now a high school basketball coach in North Carolina.
They have more people than Wyoming