A federal grand jury has begun an investigation into allegations that three Fairfax County policemen needlessly beat a 16-year-old youth they were arresting and that a county police trial board may have attempted to cover up the incident.

The officers - one of whom was earlier exonerated by a county police trial board composed entirely of police officer - have agreed to appear voluntarily before the grand jury, county officials yesterday told a federal judge in Alexandria.

Assistant U.S. Attorney Frank W. Dunham said the grand jury "will not only focus on the conduct of these three officers, but the conduct of the officers who reviewed" the incident. The jury is attempting to determine "if the police trial board acted properly or swept it (the incident) under the rug," Dunham said.

Disclosure of the grand jury investigation came yesterday morning as lawyers for the county attempted to quash a subpeona for a transcript of a statement that one of the officers made to the trial board. The officer, Keith M. Florence, made the statement under a grant of immunity from state prosecution and under a threat of losing his job, Jack Gould, assistant Fairfax County attorney, told U.S. District Judge Albert V. Bryan Jr.

Dunham said he did not know what Florence said in the statement and that was why the government was attempting to obtain it by a subpoena. The trial board's proceedings are closed and Fairfax police have refused to release details of their internal investigation into the incident.

Bryan refused the county's request, but set limits on the use of the statement in the investigation. Dunham had said that the statement would be used only to check on the officers' testimony before the grand jury and would not be used at any trial, if the officers are indicted.

The incident, which Gould said marks the first time federal authorities have investigated the county police for their conduct, grows out of the Jan. 6 arrest of Howard L. Cadle at roller skating rink in the Franconia section of the county.

Witnesses to the arrest have said they saw policemen hit Cadle repeatedly on the head and shoulders with their billy clubs. Lacy Cadle. The youth's father, filed brutality charges against the three officers, but on March. 29, Fairfax County Chief Col. Richard A. King dismissed the charges.

King said he accepted the decision of the trial board that found that Florence did not use "excessive physical force" in arresting Cadle. Brutality charges against the other two officers. Robert T. Hubbard and James F. Kelly Jr., were dismissed without a trial board hearing because of what King said was insufficient evidence.

All three officers are currently on duty on the Fairfax County force.

The grand jury probe is itself an outgrowth of an FBI investigation of the arrest, a Justice Department source said. It could not be learned yesterday who initially requested the investigation.

A Justice Department official said that the department receives between 12,000 and 15,000 complaints a year against police officers, but that only about 80 of the complaints are taken before a grand jury. About 60 of the cases result in indictments, the official said.

The official said the federal investigation is being conducted under the 1968 Civil Rights Act which makes officers who violated the civil rights of an individual subject to a fine of up to $1,000 and a year in jail.

"We're no different from any other police department in the country," said Fairfax Chief King yesterday. The grand jury investigation "of itself is not a conviction or a trial," he said.

Since King dismissed the brutality charges, Cadle's father has filed a $20,000 damage suit against the officers in federal District Court.

In their answer to the suit, the officers denied Cadle's version of the incident. They said in court papers, however, that "any injury or damage suffered by" Cadle was caused by his "wrongful acts and conduct and the willful resistance to a peace officer" in the discharge of his duties.

The force used by the officers "if any . . . was reasonable and necessary under the circumstances" and was caused by Cadle's assault and battery on the officers, according to the court papers. Their actions were lawful and in self-defense, the officers said.