Alexandria Public Safety Director Charles T. Strobel, whose actions in a police drug investigation last year are under scrutiny by a special grand jury, has applied for a job in Colorado.

Through a spokeswoman, Strobel said yesterday he applied for the job of director of Colorado's Bureau of Investigation Dec. 22, but would not resign until the controversy in Alexandria is cleared up.

City Manager Douglas Harman, whose actions in the handling of the drug investigation have been questioned by some members of the Alexandria City Council, is also seeking another job. He is in Fort Worth this week being interviewed for the post of city manager there.

Strobel's application came the day that the Alexandria City Council voted to hire an outside investigator to look into allegations that he prematurely stopped the drug investigation after the name of Alexandria Sheriff Michael E. Norris surfaced on a tape recording made by an informant.

The council later decided not to follow through on its decision, and on Jan 7. the city commonwealth's attorney asked for a special grand jury to probe the handling of the drug investigation. The grand juryt began its review Tuesday. Fairfax County Commonwealth's Attorney Robert F. Horan was appointed special counsel to assist it.

Strobel, 47, who has been police chief since l977 and Public Safety director since l983, has said that his integrity is being questioned unfairly.

In a recent interview, Strobel said that "at the very worst," a review of his actions in the drug investigation may show poor judgment, but not misconduct.

"He must feel there are some problems out there in his police department . There must be," Mayor Charles E. Beatley replied when asked about Strobel's search for a new job.

"I think the real pro is not going to look for another job; he's going to look to see what the problems are and solve them. And there's nothing I've heard so far that isn't solvable," Beatley said.

"Somebody has to start making answers. In fact, they act like they are resisting answers, and that goes for the manager too," he said.

Sheriff Norris, whose actions are also being reviewed by the special Circuit Court grand jury and who denies any wrongdoing, said yesterday that he is thinking of running against Beatley for mayor in the May city elections.

"I'm not convinced this leaderless ship is going anywhere . . . . " Norris said yesterday. He has been sharply critical of Beatley's role in the council's reaction to the allegations about the drug investigation made by a former police detective.

"This is not a joke, but I am just considering it at this point," Norris said. "I'm not actively seeking a job, but I'm equally fed up with the whole affair." Norris, a Republican, said he would run as an independent.

Beatley said he "attaches no significance whatsoever" to Harman's interviews in Fort Worth, since Harman was approached for the job before the present controversy and he has been Alexandria's city manager nine years, much longer than the normal tenure of such an official.

Beatley, a Democrat who is unopposed in the mayor's race, said he wishes Norris would run for mayor, adding: "I always perform better when I have opposition."