The first trial to be held under Maryland's nine-month-old death penalty law opened here today, a case in which William Joseph Parker, a 28-year-old vagabond fireman, is charged with the murder of a 13-year-old Annapolis girl last summer.

Judge Howard S. Chasanow has ruled that if Parker is found guilty of first-degree murder in the death of Elizabeth C. Archard last Aug. 28, the state may seek the death penalty since Parker is also charged with first-degree rape, kidnaping and abduction.

The trial was moved here the St. Mary's County seat, from Prince George's County, where Archard's body was found on Aug. 29 in a wooded area outside Bowie, because of pretrial publicity.

Today, after three hours of jury selection and brief, low-kay opening statements by prosecutor Edmund B. O'Connell Jr. and defense attorney Fred W. Bennett, O'Connell began setting the scene for the crucial police witnesses who will testify Tuesday.

O'Connell's first witness was the victim's sister, 15-year-old Lenetta Archard. The teen-ager was in tears almost from the moment she took the witness stand, as O'Connell asked her to recall Aug. 28, the last time she saw her younger sister alive.

Archard testified that on that morning she and her sister rode their bicycles into Annapolis for a dentist appointment. Lenetta Archard said after her appointment was completed she left Elizabeth at the dentist's office and went to cheerleading practice.

"Did you ever see your sister alive again?" O'Connell asked in a whisper. "No," Archard answered, burying her head in her hands as Parker leaned back in his chair and smiled.

O'Connell then called Matthew S. Kruk, a telephone line repairman. On Aug, 28, Kruk was working all day near the area where Archard's body was found and testified to hearing "about five or six gunshots," at about 2 p.m. But he also testified that the only car he saw enter or leave the area drove away about 30 minutes before he heard the shots.

O'Connell also called the two brothers who found the body on the night of Aug. 29. Finally, over defense attorney Bennett's objection, Frederick L. Jones was allowed to testify.

Jones said he had worked as a volunteer fireman with Parker in Anne Arundel County in 1978 and sold him a .22 caliber revolver that spring.

A .22 caliber revolver was found in Parker's car by police, but Chasanow has ordered it cannot be introduced as evidence because of illegal seizure.

But, over Bennett's lengthy objection, the jury of seven men and five women were allowed to hear Jones testify about the sale of the gun to Parker. The five bullets taken from Archard's body were identified as coming from a .22 caliber revolver.

Both attorneys agree that the case will turn on the statement given by Parker to detective Wallace Sibilla on Sept. 14 just before he was charged with Archard's murder.

Benneth said during his opening statement today that he would call Parker to testify but only on the "voluntariness," of his statement. "You must determine," Bennett told the jury, "whether this statement, given at 11:30 p.m. after Mr. Parker had been read his rights at 5:02 p.m., was made of free will.

"You will hear Mr. Parker testify that he had only gotten one hour of sleep the previous night, that he was exhausted because he was on medication and finally made an incriminating statement because he was worn down and the police had used three different detectives, in effect trickery, to get him to make a statement."

In testimony made in a closed courtroom in January-the judge released a transcript today after the jury was selected-Sebilla testified that Parker said he was with Archard on Aug. 28 but "blacked out," before the shooting took place.

"Next thing he tells me is that she came up to the car and he asked her if she wanted a ride in which she consented," Sebilla testified. "She got into the car and they drove out of the Annapolis area towards Governors Bridge Road. . .

"He started to make out with her by kissing and petting and then he asked her if she wanted to have sexual intercourse and she consented to it. He told me that she removed her clothes and that they made love in the front seat of the car.After they were finished she was getting dressed and at this time she stated to him that she was going to tell her father, and he asked why, and she said, well, I am just going to tell my father, and he became very upset and then he became violent. Then he stated to me that he kind of blacked out.

"I said, well, can you remember anything else. He said yes, I remember having my gun in my hand, holding it over her."