Federal prosecutors have begun investigating new criminal allegations against Dr. Murdock Head, the long-time Airlie Foundation director sentenced last month to three years' imprisonment for participating in an illegal conspiracy.

The new grand jury probe of the 55-year-old Head was confirmed by a federal prosecutor yesterday during a U.S. District Court hearing in Alexandria. Neither prosecutors nor Head's attorneys would make clear yesterday the scope of the new investigation.

Knowledgeable sources indicated, however, that one issue presented to the grand jury may center on whether Head improperly charged U.S. government agencies for excessive or fradulent expenses allegedly incurred by his foundation and affiliated enterprises, based near Warrenton, Va.

Head is currently free on bond while he appeals his Oct. 12 conviction on a single conspiracy charge by a federal jury.

He has relinquished his day-to-day duties as a professor and department chairman at George Washington University and has temporarily stepped aside as executive director of the Airlie Foundation, which he started 19 years ago.

The conspiracy count of which Head was convicted alleged that he schemed to bribe Rep. Daniel J. Flood (D-Pa.), former representative Otto E. Passman (D-La.) and other government officials and to violate tax laws. The Washington Post later reported, however, that the jury interpreted the conspiracy charge more narrowly and did not believe Head guilty of arranging payoffs to Flood or Passman.

Instead, according to The Post's account, the jurors concluded that Head had conspired to commit tax infractions, including arranging an improper $11,000 loan to a former Internal Revenue Service agent.

The jury acquitted Head of two tax-evasion charges and reported itself deadlocked on a third tax-evasion count. Judge Oren R. Lewis dismissed eight other bribery and tax-falsification charges against Head, and set aside one additional bribery count for trial possibly at a later date.

The prosecution has notified the court that it intends to ask an appellate court to overturn Judge Lewis' dismissals of the tax and bribery charges against Head. Prosecutors have not announced whether they intend to try Head on the remaining bribery count that Lewis set aside.

In an interview yesterday, Frank W. Dunham Jr., one of Head's lawyers, complained sharply about the prosecutors' move to investigate additional criminal allegations against Head. Noting that the initial 13-count indictment against Head followed an investigation of about two years, Dunham asserted, "That's enough. You don't keep on investigating him. They're treating him like he's a member of a Mafia family . . . It's a waste of government resources."

Assistant U.S. Attorney Theodore S. Greenberg confirmed the investigation of new allegations against Head during yesterday's hearing, saying, "Early next year we will present other violations . . . to the grand jury."

Among issues that appeared likely to figure in the new probe are previous allegations by prosecutors that Head established a secret "slush fund," amounting to more than $90,000, while receiving government contracts and grants for his Airlie enterprises.