THERE IS AN UGLY SPLIT in the ranks of the District's police department. Yesterday, Chief Burtell M. Jefferson's announcement of his decision to reinstate Deputy Police Chief William Trussell to previous responsibilities set off an angry walkout of homicide squad detectives from the chief's press conference; applause from top-ranking members of the deparment; and new racial tensions among the officers. Though the events leading up to yesterday's incidents were complicated, neither Mayor Barry nor Chief Jefferson should tolerate insubordination. No police department can be run effectively by rebellion.

Even though Mayor Barry has indicated that he had reservations about his chief's decision, he properly characterized the matter at this point as a management problem to be handled by the chief, rather than as a policy matter requiring the mayor's active involvement. Of course, Mayor Barry can intervene at anytime -- to overturn his chief's decision or even to replace the chief. But so long as he claims to support Chief Jefferson's actions, the mayor and the chief should join in moving against any rank-and-file revolt by a faction in the department.

The original charges by homicide squad detectives against Deputy Chief Trussell, who was chief of detectives and who is white, were that he was "incompetent" and that he had made racial slurs. In May, at the mayor's urging, Chief Jefferson, who is black, appointed a three-member panel to investigate. That panel voted 2 to 1 against reinstating Trussel -- but on grounds that the controversy and Mr. Trussell's reactions to it, rather than his competence or the alleged racial slur, would affect his ability to command officers. But the chief reportedly concluded that his deputy had been quoted out of context or misunderstood and should be given a chance to resume command. On Thursday, word of the chief's decision prompted an angry call from the International Brotherhood of Police Officers for Chief Jefferson to retire; that, in turn, prompted the D.C. Afro-American Police Officers Association to charge that the position of the Brotherhood's white leadership does not respect the views of either the black officers on the force or the community at large.

If the racial aspects seem confusing here, it is because race is being used by all sides in the Trussell affair to conceal internal disputes over personalities and policies. At this point, however, the mayor says he has confidence in his deputy chief. Certainly that constitutes a chain of command -- which should not be broken by subordinates in rebellion.