D.C. Mayor Sharon Pratt Dixon, reacting to the double homicide of an elderly couple, ordered police yesterday to step up patrols around the Arthur Capper Senior Facility near the Washington Navy Yard in Southeast.

The announcement, made during a hastily arranged visit to the building by Dixon, D.C. Council Chairman John A. Wilson and senior police commanders, resulted in the posting of at least one officer in the immediate area.

The D.C. Department of Public and Assisted Housing has long sought police patrols for some of its troubled buildings, and officials at the agency were encouraged by yesterday's announcement.

A spokesman for Dixon said later the mayor is interested in coordinating security efforts between the police department and the housing agency, and meetings to discuss the extent of the cooperation will take place in the next few weeks.

For now, the beat patrol officer already assigned to the area around Sixth and L streets SE will work with the building's security. Housing officials, also reacting to the two slayings, had increased the guards in the building from one to two.

This week, as part of across-the-board cuts, Dixon said the police department could not hire 200 more officers. A further reduction in the force through attrition could cut staffing by at least 200 more. Vada O'Hara Manager, a spokesman for the mayor, said Dixon's plan places "a high premium" on moving officers from desk duty to street patrols.

But police officials, while quick to boost patrols at Arthur Capper, privately questioned whether this could be done citywide. Although it is too early to determine exactly what the police department's role will be, one police official said patrols in many buildings would not be realistic in light of the cutbacks.

"For every police officer that you assign, for every beat that you assign, you're talking 4 1/2 police officers to fill that assignment 24 hours a day, seven days a week," said the police official.

Police yesterday had no new information on the killing of George Bailey, 82, and his wife, Maggie, 75. The elderly couple were found inside their apartment on Wednesday, at least four days after they were stabbed to death.

Although there is no evidence that the security in the building played a role in the slayings -- police said the Baileys' apartment was not broken into -- residents maintain that more guards are needed. Several people questioned the performance of the company that provides the guards, and Dixon at one point said the service "has not been adequate."

Officials at Eastern Shield Security Co., which received a District contract for 20 buildings, could not be reached for comment yesterday.

As in many other public buildings, housing officials said some Arthur Capper residents violate policy and allow relatives to move in for stretches at a time, often bypassing security by opening doors designed for emergency use only.

The public housing department's acting director, Benjamin Johnson, told seniors on Thursday that more guards would not ensure a safe building unless this practice is halted. Several residents cited this yesterday as a major reason for crimes on the premises, which they said include petty theft, beatings and possibly the killings this week.

"It could be somebody in the building. We don't know. We don't know," said Ada Clinksdale, a resident.

Seniors remembered Anne Buford, 93, who was found strangled on the fourth floor in January 1989. That killing raised similar questions about security and prompted an increase in patrols, an experience that left some seniors skeptical about promises of improvements.