The presidential commission investigating the March 28 accident at Three Mile Island has asked Congress for power to grant its witnesses immunity from prosecution in exchange for their sworn testimony about what and who caused the accident.

"Suppose there's criminal negligence involved here and suppose there's an employe who comes to us and he takes the Fifth Amendment, for whatever reason," Dr. John Kemeny, president of Dartmouth College and chairman of the President's Commission on the Accident at Three Mile Island, said recently in an interview. "We want that employe to talk to us; his testimony is crucial to our charter."

Besides the power to grant immunity, Kemeny said the commission has asked for strong subpoena powers and the power to take all testimony under oath. He said the first and perhaps toughest task the commission has is to find out everything it can about what caused the near-disastrous nuclear accident 10 miles from the Pennsylvania state capital of Harrisburg.

"A crucial thing for a plant operator is that even if he's willing to testify, you subpoena him, not to punish him, but to protect him," the Hungarian-born Kemeny said. "The fact that you subpoena him and put him under oath makes him kind of immune from somebody higher up in the company saying 'Now why did you say that?' The answer is 'Because I had no choice.'"

Kemeny said the commission plans to gather all its facts about the accident in the next four months. He said it wants to know to what extent design error, human error and equipment failure caused the accident, and to what extent the accident could and should have been anticipated.

"My first impression is that people really did no expect something this serious to happen, I really think they were taken by surprise," Kennedy said. "One of the things we have to probe in very great detail is, did something very unusual happen here that they have the right not to expect or was this something they should have prepared for?"

Kemeny said the commission staff is in the midst of assembling five teams to deal with what he called the five main issues in the accident. In addition to its causes, he said there are the question of nuclear safety "in the broadest sense," the question of real and potential danger that the accident posed to public health, and two issues that might be the most difficult to explore.

He said these were the psychological impact the accident had on the public and whether accurate and timely information about the incident reached the public.

"This last question is one that troubles President Carter very much," 'Kemeny said. "The fact that he has mentioned it a lot tells me I think he thinks the answer is no."

The commission's first hearings beyond its first get-started sessions will be May 17, 18, and 19 in Middletown, Pa., where the shutdown Three Mile Island nuclear plant is located. The first day will be spent hearing state and local officials and touring the stricken plant.

The second day will involve witnesses from Metropolitan Edison Co., the operator of Three Mile Island. Kemeny said he wants to hear from everybody, "from the executives who manage the company to the operators who pushed the buttons" the morning of the accident. The third day the commission will listen to the general population in and around Middletown.

Kemeny defended the makeup of the 11-person commission, which includes one housewife, one nuclear engineer and one physicist.

"I think the center of gravity of this commission is just right," he said. "I think it would be wrong for this commission to consist of a bunch of engineers. We're sort of a national jury on this issue and would you want the jury to consist of experts? I think it would be a mistake; you want the average American to believe what this commission says." CAPTION: Picture, DR. JOHN KEMENY . . . "We're sort of a national jury"