The Justice Department announced yesterday that it would not prosecute a Dallas policeman for the 1973 shooting death of Santos Rodriguez, a 12-year-old Mexican-American whose case has become a national issue for Hispanic groups.

Attorney General Griffin B. Bell approved a recommendation against federal prosecution, a spokesman said, because the police officer, Darrell Cain, already is serving a five-year prison term on a first-degree murder conviction in a Texas state court, and because of legal problems in reopening the five-year-old case.

The Rodriguez case has been an especially sentitive one because Mexican-American leaders showed President Carter color photos of the dead boy last month in Houston. Rodriguez was shot as Cain played Russian roulette with a .357 magnum revolver while the youth sat handcuffed in a police car.

Vilma S. Martinez, president of the Mexican-American Legal Defense and Educational Fund, said yesterday that the Justice Department decision was "frightening."

Referring to the administration's criticism of the Soviet Union's charges against dissident Anatoly Scharansky, she said: "I wish the president were as interested in the human rights of Santos Rodriguez as he is in those of Mr. Scharansky."

The Justice Department announcement noted that the "senselessness of the crime" and the victim's age had focused public attention on the case and made the decision not to prosecute "particularly difficult." But spokesman Terrence B. Adamson said yesterday, "We simply cannot make decisions based on public opinion polls."

Justice investigated the shooting in 1973 but department policy at the time prohibited a federal civil rights prosecution inna case where there had been a successful state prosecution.

The case reopened because Bell changed the "dual prosecution" policy in February 1977 to allow federal indictments "likely to vindicate rights."

Applying the new policy retroactively to the Rodriguez case reaised questions about selective prosecution and due process, the Justice announcement said.

The legal problems collectively raised questions about the "fairness and wisdom" of such a dual prosecution, Bell said in the statement. He emphasized, however, that the department would continue to use such dual prosecution to protect the civil rights of Hispanics and other.

Department officials said the recommendation against prosecution was approved up the chain of command from the U.S. attorney's office in Dallas, through the civil rights division criminal dection and Assistant Attorney General Drew S. Days III, to Deputy Attorney General Benjamin R. Civiletti.

Bell, who is in Australia on a three-week speaking tour-vacation, made the final decision overseas after studying some of the legal issues, Adamson said.

White House press secretary Jody Powell was informed of the decision yesterday in Bonn, Adamson added. Carter had promised the Hispanic leaders in Houston last month that Bell would take personal charge of the case.

The Justice Department has been reviewing some 60 cases of alleged brutality against Hispanics and has been under increasing public pressure from civil rights groups.

Martinez said the decision revealed "the administration's perception of the worth of a Mexican-American life." She said she was "appalled to see such blatant violation of human rights in our own country."