An off-duty D.C. police officer was shot and seriously wounded last night by a robber who apparently held him up while he and his wife were in a park just across the Anacostia River from RFK Stadium.

Bleeding profusely from a wound in his right side, Officer Michael K. Smith collapsed across the street from the park, in front of the house of a woman who said he told her that his assailant or assailants "didn't have to shoot me . . . I gave them the money."

The woman, Mrs. Louis Thompson, said she found the wounded 6th District officer and his wife outside her house at 103 Anacostia Ave. NE about 10:30 p.m. after she heard what she described as frantic knocking at her door accompanied by cries for help.

Smith, 36, a member of the force since 1969, was flown by U.S. Park Police helicopter to the Medstar Unit of the Washington Hospital Center, where he was listed in fair condition early today.

Using dogs and a helicopter, police searched for a suspect for hours after the shooting in and around the site of the incident, a strip of greenery known as River Terrace Park, which lies between Anacostia Avenue and the Anacostia River just north of Whitney Young Memorial Bridge.

As she tended the officer last night, Thompson said, he told her that he and his wife had been in the park between 10:20 p.m. and 10:30 p.m. While Smith's wife sat on a swing, he walked to a nearby stream where he was apparently robbed and shot.

Shortly afterward, Thompson said, she opened her front door in response to the knocking and found the officer's wife, who cried: "Help, my husband has been shot."

Thompson said the officer, who had been facing her, turned and she could see blood staining the back of his light colored T-shirt. He fell to the ground, she said, and lay on his side, partly on her lawn and partly on her front walk.

As she went back inside and began to call police, she said, Smith's wife urged her to "please hurry" and to "tell them he's a police officer." Then she said, while the officer's wife went inside to talk to authorities, she went back outside, loosened Smith's belt, and using a towel, tried to stanch the flow of blood from the officer's wound.

Smith told her he was in pain. "I just can't get comfortable," he told her as he lay on the ground. Within minutes, the Park Police helicopter landed across the street in the park to take Smith to the hospital.

A D.C. police spokesman said Smith's service revolver was found later last night in his car, parked near the scene.