C3 Inc. said yesterday that the Justice Department has dropped one of its two criminal investigations of allegations of impropriety over two contracts the company had with the Defense Department.

In a brief announcement, C3 said a representative of the U.S. Attorney's Office for the Eastern District of Virginia had told the Reston computer systems company that the government has terminated its investigation of alleged improper conduct in connection with the company's obtaining a Department of Army contract at the White Sands Missile range. C3 said the U.S. Attorney's representative said that no indictment will be sought as a result of this investigation.

However, the company noted, the U.S. Attorney's Office has not concluded its investigation into another C3-Army contract with the Defense Supply System-Washington. The company had earlier disclosed that a grand jury had been called to examine the allegations surrounding both contracts.

"The company hopes that this investigation will be terminated shortly," C3 said. Joseph J. Aronica, chief of the criminal division of the U.S. Attorney's Office for the Eastern District of Virginia, declined to comment on when the latter investigation would be concluded or what its outcome would be, only the probe "is still continuing."

C3's troubles began in October 1982 when C3 was suspended from bidding on government contracts for two weeks after the Army accused it of "making false statements and claims" on an Army contract. The suspension was lifted when the Army decided that the fact-finding connected with the appeal of the suspension would jeopardize an investigation of the charges. It is this investigation that is still pending.

A civil lawsuit relating to the same contract is still pending in the U.S. Claims Court as well.

The Army again suspended C3 from bidding on government contracts in January 1983, charging that there were improprieties in connection with C3's contract to supply computer equipment to the White Sands Missile Range in New Mexico. The Army cleared C3 after a four-week investigation. Although the U.S. Attorney's Office dropped its investigation of this contract, the company noted that both C3 and the Army still have civil claims against one another regarding this contract.