The Justice Department said yesterday that it has found not evidence of espionage in the case of the 25-year-old nuclear missile officer who was charged Friday by the Air Force with making unauthorized visits to the Soviet Embassy here.

Department spokesman John K. Russell said that the case was never formally referred to federal prosecutors, but added, "We are advised of it, it is a military matter. We're not investigating it, we're not going to prosecute it, for sure."

Russell declined to reveal details that would explain why the young officer, 2nd Lt. Christopher M. Cooke, made three trips to the Russian Embassy last December and during May.

"What I'm saying is that we don't have a case," Russell said. "We have taken a look at the facts of the situation and the legal issues and consider it to be a strictly military matter and not in the jurisdiction of the Department of Justice."

If there were evidence of espionage, Russell said, Justice Department officials would take jurisdiction of the case, as the department has in the past. "We do not think we have an espionage case in this matter," he said.

Cooke, the deputy crew commander of a Titan nuclear missile team stationed at McConnell Air Force Base near Witchita, Kan., was charged with violating Air Force regulations against unauthorized contact with representatives of a communist government.

Only sketchy details of Cooke's activities have been pieced together from interviews with his family, Air Force attorney and friends, but they suggest that Cooke was discovered in some unauthorized activity by Air Force security personnel. He was then enlisted to cooperate in an Air Force investigation for which he was promised immunity from prosecution and an honorable discharge, according to his lawyer and parents.

But whatever agreement Cooke had or thought he had seemed to evaporate with the filing of the charges.

Cooke, who had access to top secret codes and weapon technology in the Titan silos beneath Kanasa farmland had unsuccessfully sought a career in the Central Intelligence Agency, his parents of Richmond, Va. said.

"I'm well aware he did something he shouldn't have done," Mrs. Richard C. Cooke told United Press International, adding, "I'm in disagreement with how the Air Force handled this."

Cooke's father, asked if he thought his son was involved in a security breach, said, "I had him for 25 years and there is no way of knowing positively. I don't have any doubt that there is something more to this than what we know. He wasn't in it [any unauthorized activity] to make money I can't conceive of that, I know."

A native of Portsmouth, Va., Cooke was graduated magna cum laude from Old Dominion University and joined the Air Force in December, 1979.

James Litsey, a former Titan missile commander and Wichita lawyer, said yesterday in an interview that he thinks the Titan security could have been seriously compromised by Cooke's visit. He said Cooke's job required a top-secret security clearance and gave him access not only to secret code books necessary in the launch cycle of a Titan, but also important code message formats.

"To me, that's probably the greatest of the potential harms," Litsey said. "If they [the Russians] get a message format, SAC [Strategic Air Command] will have to redo everything from the ground up."

Defense Department officials have pointed out that the firing codes themselves are changed frequently. But the formats, the numbers, kinds and order of words used in a code, are not changed often.

During an actual nuclear crisis, Litsey said, Russian knowledge of the code formating system could allow the Soviets to send bogus radio messages to Titan silos with authentic-sounding launch orders. Such a tactic could cause the missile crews to "stop and go through the code book to see if it was a valid message or not."

The Russians "could use it to utterly confuse the retaliatory forces," Litsey said.

The Titan is the oldest missile in the American nuclear arsenal and carries the largest warhead. Cooke was assigned as the second-ranking officer in a crew of four that mans each of the 17 silos operated around the McConnell base.

Cooke remained in custody at McConnell awaiting the decision of Brig. Gen. Elmer T. Brooks on whether to release him from detention pending a military trial.

Cooke's mother told United Press International that the FBI contacted another of their sons, Richard Cooke Jr., in March and questioned him about his elder brother's financial status.

Air Force security men searched the Cooke home twice during May, Mrs. Cooke said. Cooke himself was detained during most of May at Langley Air Force Base in Virginia.