A former Alexandria police detective who has accused Public Safety Director Charles T. Strobel of cutting short a police investigation last year into drug dealing, yesterday went before a special grand jury that is reviewing how that investigation was handled.

The former investigator, Charles Cox, was among eight witnesses who were sworn in yesterday before the 11-member panel during its first day of hearing testimony. None of those present would discuss the secret proceedings.

The special grand jury, impaneled Jan. 15, is charged with reviewing Cox's allegations that an investigation into suspected drug use by Alexandria City Sheriff Michael E. Norris and others at a restaurant on South Washington Street was ended despite promising leads.

Strobel, who has maintained that he is innocent of any wrongdoing, and Norris were among those called to appear yesterday. Strobel was present for about half an hour in the morning, and Norris said he was sworn in but did not testify yesterday.

The six others included Cox; Mary Craig, his lawyer; a civilian informant who worked with Cox on the investigation; Keith Price, a former housemate of Norris; Lt. Arthur Bratcher, who was head of the narcotics squad, and Sgt. Richard Lloyd, another member of the squad. Craig said she and her client testified for several hours.

It is not known whether Price, Bratcher or the informant gave testimony yesterday, but all three were present most of yesterday in a closed section of the Alexandria Courthouse.

At least four more witnesses have been asked to appear today. They include police investigator Joseph Morrash and Patrolman Morton M. Ford, both of whom have joined Cox in alleging that the drug investigation was halted prematurely. Also scheduled to appear are Lt. John Stedman, head of the police department's personnel and training section, and patrolman Philip Adcock, who worked with Cox on the drug investigation.

The special grand jury was requested Jan. 7 by Commonwealth's Attorney John E. Kloch, who had been asked to review allegations surrounding the drug investigation by City Manager Douglas Harman.

Harman's request followed a contentious City Council meeting Jan. 3 at which the council failed to follow through on an earlier decision to conduct its own investigation of how the police inquiry had been handled.

Under Virginia law, a special grand jury is authorized to investigate allegations of wrongdoing. It cannot return indictments, but may refer cases to a regular grand jury.

Mayor Charles E. Beatley and Democratic councilman Donald C. Casey have said they still would like to see the council do its own review of how the investigation was handled by city manager Harman and the police department. Both officials have been critical of the fact that Harman, who appointed Strobel, did not inform them of the investigation. It was being conducted while the council was debating whether to consolidate the sheriff's office into Strobel's Department of Public Safety.

The controversy appears likely to be a major issue in the upcoming City Council elections next May.