Alexandria's City Council will meet in special session tonight amid simmering disagreement among its members over the scope of an independent investigation it ordered into the handling of a drug investigation by the city police department.

One council member, Margaret B. Inman, wants the council to reconsider its Dec. 22 decision to have an investigation. In a letter sent yesterday to her six council colleagues, Inman said she was "convinced . . . council is embarked on an illegal, lengthy, costly and destructive course" that might "brutalize" its staff. She said the allegations ought to be considered by the city commonwealth's attorney, John E. Kloch.

Tonight's meeting, called by Mayor Charles E. Beatley, is intended to make formal the hiring of District lawyer Abbe D. Lowell as the council's investigator and to decide what the scope of his investigation should be, as well as the procedure and format he should use. Beatley said he did not want to wait until the scheduled Jan. 8 council meeting to make those decisions.

Lowell was selected unanimously by the council Dec. 22 by the council to investigate allegations reported in a local newspaper, the Alexandria Port Packet, that Alexandria Public Safety Director Charles T. Strobel prematurely terminated a police investigation into possible cocaine dealing last year after the name of a city official surfaced on a tape recording supplied by a police informant.

"I called the meeting because I had heard that councilman Carlyle C. Ring wanted to have a session with the attorney before he started out," Beatley said. "I have a feeling that behind this is the feeling that the investigation is not necessary."

Councilman Donald C. Casey and Ring had a sharp exchange at the Dec. 22 meeting, accusing each other of leaks of sensitive information relating to the drug investigation. They are expected to disagree further over the council's mandate for Lowell.

Ring said the purpose of the investigation "is to clear the reputations of those whose reputations have been muddied."

Casey has said the allegation that the drug investigation was stopped prematurely "is entirely accurate and there's more to it than that."

The council also has ordered an investigation into the involvement of City Manager Douglas Harman and Sheriff Michael E. Norris in the drug investigation. Harman is Strobel's immediate superior and Norris' name was the one heard on the tape recording. Both Strobel and prosecutor Kloch have said repeatedly that there is no evidence of criminal wrongdoing on Norris' part.

Lowell immediately began his investigation after the council's action Dec. 22, meeting with Beatley first. But a meeting between Lowell and Casey set for last week was called off after Ring objected to Lowell's activities.