A MISSION to China undertaken by the District's assistant director of corrections, Gwynne Washington, has provoked a small controversy, but perhaps not a big enough one. Mrs. Washington runs a vocational and educational training program at the city's Lorton complex in Fairfax County, and she has been on a three-week taxpayer-paid trip to China organized for the purpose of ''informational exchange'' by a group called Global Interactions.

In bidding Mrs. Washington bon voyage, a city official was quoted as saying that China is in a period of great change and ''needs some expertise from a proven system.'' No doubt. But that only sharpens the question of how the Chinese came to seek advice from a system -- the District's -- that has reeled from crisis to crisis and currently is being held in contempt of court for its inadequate response. It is a source of further wonder and embarrassment that the particular program in Mrs. Washington's charge, one that Global Interactions describes as ''an example of what America is doing about prisons,'' has come under severe criticism for inefficiency and low inmate participation and is currently being audited by the General Accounting Office. The assistant director herself testified last spring before a grand jury probing alleged corruption in the program by city officials.

Something else about this mission is even more astonishing. It is that an American city operating under the democratic system could, by an ''informational exchange'' of this sort, blindly lend itself to ''improving'' and legitimizing a criminal justice system that flouts the rule of law as Americans know it. No doubt there is a level on which professionals -- professionals wearing blinders -- enjoy and profit from exchanging technical information. But why in the world would Americans want to help China, a police state, fine-tune the machinery of totalitarian compulsion, which is a fair description of what this mission is about? Is the next District prison informational exchange to be conducted with South Africa?