A jury of seven women and five men was selected yesterday to hear the espionage case against retired Navy communications expert Jerry Alfred Whitworth in federal court in San Francisco.

U.S. District Judge John P. Vukasin Jr. ordered the 12 jurors and six alternates to return March 24 for opening statements in the trial of Whitworth, the last of four persons charged in the Walker family spy ring to face trial.

Vukasin ordered the jurors not to discuss the case or read about it, saying, "You have a serious responsibility." Among those chosen after eight days of jury selection were a bank officer, an economist and a sanitation worker.

Whitworth, 46, a retired senior chief radioman from Davis, Calif., is charged with 13 counts of espionage and tax violations.

The government alleges that Whitworth received $332,000 from admitted spy John Anthony Walker Jr. to pass highly sensitive information about Navy codes and coding machines to the Soviet Union in a conspiracy that lasted from 1974 until Walker was arrested last May 20.

Vukasin indicated that he expected to rule today on whether prosecutors may use a critical piece of evidence against Whitworth -- a series of four letters, signed "RUS," that were sent to the FBI's San Francisco office in 1984.

The government contends that "RUS," who offered to expose a "significant espionage system," is Whitworth. Defense lawyers argue that there is no adequate proof that Whitworth wrote the letters and that they constitute a virtual confession that would hurt Whitworth's chances of a fair trial.

The trial is expected to last two to three months. The government's main witness is to be John Walker, who pleaded guilty to espionage in federal court in Baltimore on Oct. 28.