NOBODY IN Alexandria seems to know precisely what it's all about, but city hall is in an uproar these days -- with tempers boiling, fingers pointing and charges flying back and forth between key figures in the local government. While there has been no concrete evidence so far of criminal or even bureaucratic wrongdoing of any serious nature, the air has been filled with allegations that should be investigated as impartially, thoroughly and swiftly as possible. And because they involve the conduct of a police drug investigation and the reactions of various city officials, somebody other than city-government-connected lawyers and authorities should be requested or assigned to investigate.

It all began last month when a local newspaper, the Alexandria Port Packet, published allegations that a drug investigation ad been halted prematurely by Police Chief Charles T. Strobel after the name of Sheriff Michael E. Norris turned up on a police informant's tape recording. Chief Strobel has said repeatedly that there is no evidence of any criminal wrongdoing on the part of the sheriff; and Sheriff Norris has denied wrongdoing, bitterly attacking what he has called "an unprecedented witch hunt."

The allegations were brought to the attention of the Alexandria city council by member Donald C. Casey, who has urged an independent investigation into the drug case. On Dec. 22, the city council voted to hire outside counsel to investigate the office of the sheriff, City Manager Douglas Harman and the police chief. But this week the council deliberated for more than two hours without deciding what to do; at that point, Mr. Harman said he will refer questions relating to the the conduct of the police drug investigation to the commonwealth's attorney/city prosecutor. Mr. Harman told the council: "As one individual smeared by this whole thing" and who has had his name "dragged through the media . . . I am tired of this media circus."

Whatever it may be, someone other than the city prosecutor should take over the investigating. The city prosecutor already has made a judgment after reviewing much of the material relating to the drug investigation earlier, at the request of police investigators who were upset at how the drug investigation was being handled by the chief. It may well be that all of this back-and-forth is nothing more than hot air and personal smears. But should the police have dropped that drug investigation? In fairness to everyone involved -- including every resident of Alexandria -- an independent investigation should be made as originally voted.