A Prince George's County police detective testified today that William Joseph Parker told him he "blacked out" after having sexual intercourse with 13-year-old Elizabeth C. Archrd on Aug. 28 and awoke seconds later to find her dead.

Parker is on trial here on charges of kidnaping, raping and murdering the girl.

Detective Wallis A. Sibila testified that on Sept. 14, 1978, Parker told him that he had taken Archard in his car from an area about a mile from her home in Annapolis to a wooded area near Bowie and had sex with her.

"When they were finished, he said they got dressed and she stated to him that she was going to tell her father," Sibila testified. "He asked her why and she said she was just going to tell her father and he became very upset and then he became violent and kind of blacked out."

Sibila said Parker told him the next thing he remembered was "standing next to the car having my gun in my hand and holding it over her."

In a statement which he said he typed immediately after talking to Parker, Sibila wrote, "he (Parker) remembered reaching under the seat and retrieving the gun. His mind went blank and the next thing he knew Elizabeth was dead." That statement was introduced into evidence today.

Sibila was one of three key police witnesses to testify today, the third day of the trial.

If convicted, Parker, a 28-year-old volunteer fireman, could become the first person to be given a death sentence in Maryland under the state's nine-month-old death penalty statute.

Today, as Parker sat, his hands folded, staring at each witness; Sibilia, Detective Tony R. Tucker and Detective Earl W. Jones testified about the events leading to Parker's arrest.

Johns said he had two officers ask Parker to come to headquarters on the evening of Sept. 14. After reading him his rights, Jonesquestioned Parker and asked him to write a statement, the detective testified. When Parker repeatedly denied involvement, Jones said he asked Tucker to question him at about 10:30 p.m. - 5 1/2 hours after Parker came to police headquarters.

Tucker said that after 45 minutes, Parker asked to speak to Sibila, whom he knew through his work as a fireman.

"When I went in," Sibila testified, "I asked how he (Parker) was feeling, and he said not well, that he was having problems with his girlfriend." He said he had waited for her a while, then called her. He said he went to meet her near Spa Road. He said she walked up to the car and he asked her if she wanted to go for a ride and she said yes and got in the car. He said they drove to Governors Bridge Road."

Sibila said that at that point, thinking Parker had been talking about his girfriend, he said, "by we, who do you mean?" Parker answered, "the Archard girl and I," Sibila said.

Sibila said that Parker told him he would put his statement in writing only for Sibila or Tucker, whom he also knew personally. Tucker then returned and took the written statement.

Reading from the statement, in which Parker virtually repeated the story he had told Sibila, Tucker quoted, "We had sex in the front seat of the car. She was going along with this. Nothing was forced. Then we got dressed and she said something like she was going to tell now, I guess she was mad . . . Then I blacked out or a memory lapse. I was upset cause she told me she was 13 years old . . . The next thing I remember I was getting in my car. I drove right on Governors Bridge Road, back to Harbor Hills. I don't remember what time it was, it was still daylight. She wasn't with me."

Archard's body was found the following day in the wooded area. She had been shot five times.

Parker is expected to testify Thursday.