A peeping Tom who peers in a bedroom window and then opens fire on the person he's watching may have shot five Southeast Washington residents in the last six weeks, District police said yesterday.

The shooting of an off-duty District police officer, wounded late Wednesday when a shot was fired through the bedroom window of her Southeast apartment, has been linked to four other incidents since early September, police said.

Officer Kelli Williams, 26, who lives on 10th Place SE, was in stable condition at Greater Southeast Hospital yesterday, a hospital spokeswoman said. Williams, a patrol officer in the 7th District for three years, was grazed by the bullet, police said.

The shooting, which occurred shortly after 11:30 p.m., strongly resembles four other Southeast shootings, police said.

In each of those incidents, an unidentified prowler preyed on women in first-floor Southeast apartments with bedroom windows either open or not covered by shades or curtains, police said. In another incident, an unidentified man shot a woman working alone in an office of a Southeast tourist home.

All of the shootings have occurred late at night or before dawn, police said. No victim was injured critically.

"It appears we're dealing with a very deranged individual," Capt. William White III, a police spokesman, said at a news conference. "There appears to be no motive whatsoever. We have seen nothing like this before."

White said police patrols in Southeast have been significantly increased in response to the shootings, which he said were being investigated by the 7th District and the department's Sex Offense Division.

Police advised Southeast residents, especially women living in first-floor apartments, to be sure the windows and doors of their homes are locked before they go to sleep.

The victims appear to have been selected at random, White said, and the incidents have not been confined to any neighborhood.

Before Williams was shot Wednesday night, White said, police had started to discover a closely related pattern of Southeast shootings in the last six weeks. Police related the these incidents:

On Sept. 5, at 4:40 a.m., a man and woman in bed in an apartment in the 3300 block of 22nd Street SE, were shot by a prowler outside their window. Two days later, at 5:30 a.m., a man and woman in their apartment in the 2000 block of Shipley Terrace SE heard a noise outside their bedroom window. As the man walked toward the window, he was shot.

Two other such shootings occurred Sept. 18. At 12:10 a.m. a witness saw a man peeping into a bedroom window in the 2800 block of Second Street SE. The witness then saw the man fire a shot into the bedroom. No one was injured.

About a half-hour later, a woman working alone in an office of a tourist home on Parkland Place SE saw a man peer in the office window. She screamed, police said, and the man shot her once in the arm and fled.

White said police are preparing a psychological profile on the man they believe to be responsible for the shootings and asked anyone with information about the incidents to call Crime Solvers at 393-2222.