Christopher M. Cooke, the 2nd lieutenant accused of visiting the Soviet Embassy here without notifying his Air Force superiors, wanted to work for the CIA, his father said yesterday. He applied for a job with the CIA after he finished graduate school, and last fall received a letter asking him to go to the agency's headquarters for an interview.

Richard Cooke doesn't know what became of that request. "Every time I asked him about it, he'd say that's top secret," Cooke recalled yesterday from his home in Richmond. "But that doesn't sound to me like the kind of guy who would walk into the Russian enbassy three times in broad daylight."

"Maybe he was working for another agency, or trying to pass false information," the father continued. "It all sounds very strange to me."

The case of Cooke, a 25-year-old commissioned officer who serves as a deputy crew commander at a Titan nuclear missile site and allegedly visited the Soviet Embassy three times between December and May, is clouded with mystery: What information would someone in his position have to offer? Why would they be so open in their approach?

There were few answers yesterday. The CIA and the Soviet Embassy refused official comment.

"The problem is so many people come to the embassy bringing crazy plans. It's a headache for us," the embassy duty officer said. "So we'll have no comment."

A source close to the CIA said the letter to Cooke "must be pure coincidence. Anything as crude as walking into the Soviet Embassy wouldn't be sponsored by us."

Cooke was charged with "violating Air Force regulations which require reporting all contacts with representatives of a communist country" late Friday after being held for almost a month at Langley Air Force Base in Hampton, Va., and McConnell Air Force Base near Witchita, Kan., for interrogation and mental testing.

If convicted, the charge carries a maximum penalty of two years at hard labor, forfeiture of pay and dismissal from the service.

An informal pre-trial conference was held late yesterday at McConnell. The case now goes to Brig. Gen. Elmer Brooks, Cooke's commander, according to officials at the Strategic Air Command in Omaha. Brooks will determine if Cooke will continue to be held in pre-trial confinement.

Cooke was a deputy command officer in a four-member crew, made up of two officers and two enlisted men, who worked in a confined underground chamber at one of the 17 Titan missile sites at McConnell. The Titan is the largest and oldest missile in the U.S. arsenal and packs the biggest atomic punch.

As one of two officers who operate keys that can activate the missile, Cooke would know procedures involved in firing the Titan and have detailed knowledge about how the system works, according to Defense Department officials. But he would not possess key codes used in firing orders from higher authority.

These codes are kept locked, at the launch silo, until orders are sent from the president, and are changed frequently, the Associated Press reported.

"It's all done with very sophisticated electronic machinery. Nobody who knows what the codes are one day knows what they'll be the next," said one former high intelligence agency strategist. "I'd love to get my hands on a Soviet second lieutenant in one of their silos, but it's not like he could give you the family jewels."

Walking into the Soviet Embassy in full view of U.S. intelligence gathering cameras "is certainly not the way to go about it if you're interested in espionage," the former official said. "I can see going in there in a confused state of mind. Why the Soviets tolerated him, I don't know."

Cooke, who is unmarried, joined the Air Force in December 1979 and was assigned to McConnell in June of last year after completing Officer Candidate School and missile training. He grew up in Portsmouth, Va., one of five children, and worked summers in the small electronics firm his father then operated there. At Cradock High School, he worked on the school newspaper and was the No. 1 ranked player on the school tennis team.

He graduated magna cum laude from Old Dominion University in Norfolk with a major in political science, and at one point represented the school in a mock United Nations conference in New York. "He was assigned the anti-communist side in a debate there and his side won," his father recalls.

He received a masters degree in foreign relations at the College of William & Mary in Williamsburg, where he toyed with becoming a college professor, doing intelligence work, or joining the Foreign Service, according to friends.

"He was just a very normal kid," said Tom Stenzel, Cooke's doubles partner on his high school tennis team. "I see a big chance of some logical explanation of this all. I'd love to hear his side of it."

Cooke's parents yesterday maintained that their son and his Air Force lawyer, Capt. Frank Pedrotty, told them the Air Force had signed an agreement giving Cooke immunity from prosecution and an honorable discharge in exchange for his cooperation in the case, but then reneged on the agreement.

Until Friday, the parents said they had talked with their son each evening and he had told them if he failed to call, even one night, they were to notify the press about the agreement. Asked about the charge, an Air Force spokesman said, "no comment."