The Defense Department said yesterday that it is investigating allegations that a senior contract auditor "improperly solicited" funds from employes to cover legal expenses of his former boss, fired for trying to punish a whistle blower.

The announcement followed release of a letter from Robert D. Bickel, the Defense Contract Audit Agency's deputy assistant director of operations, calling on recipients to display "personal salesmanship" in raising funds for former DCAA director Charles O. Starrett Jr., who is appealing his June 17 firing.

"I am asking each of you to go back through your network and by word of mouth or whatever just quietly restate the case," said the handwritten letter dated Sept. 9 and released yesterday by the Project on Military Procurement, a group that monitors Pentagon activity.

"Arm twisting is out, but it wouldn't hurt to let everyone know we have had a slim showing to date and in case they have forgotten . . . let's get those checks rolling in," Bickel wrote.

Defense Department standards of conduct prohibit officials from using their positions to "induce, coerce or in any manner influence any person, including subordinates, to provide any benefit, financial or otherwise, to themselves or others."

Bickel, the DCAA's fourth-highest ranking official, did not return a reporter's telephone calls yesterday. But, in an earlier interview with States News Service, he was quoted as saying of the Sept. 9 appeal:

"It's not a fund-raising letter. It's just something I sent out to people who had agreed to help me in the cause."

Bickel, confirming that some DCAA administrators are raising money from employes, described the effort as a "private venture by a group of friends and private citizens who have every right to do what they want."

Bickel's letter was written to the Federal Managers Support Association Fund-Raising Network, a private group of active and retired DCAA employes established in July. Its aim is to raise $35,000 to help finance federal court appeals by Starrett and two DCAA Atlanta regional officials demoted in the same case.

The three were disciplined by the Merit Systems Protection Board in June for retaliating in 1983 against George B. Spanton, the DCAA resident auditor at the Government Products Division of Pratt & Whitney, a subsidiary of United Technologies Corp. in West Palm Beach.

Spanton was reassigned to the West Coast after producing several audits critical of the jet-engine manufacturer's pricing. Then he went public with his findings after concluding that the DCAA was ignoring them.

Spanton said in a telephone interview yesterday that copies of Bickel's letter were sent to him by ex-colleagues in DCAA regional offices in Boston, Chicago and Atlanta. He said the letter, beginning "Dear Workers," had apparently been circulated to employes by members of the fund-raising association.

"I'm sure they feel under the gun to contribute because the boss knows who's willing to support the project," Spanton said.

The DCAA, which has 4,200 employes, audits the Pentagon contracts with weapons manufacturers to make sure overhead charges and other expenses are reasonable.

In response to inquiries yesterday, a Pentagon spokesman said the department's inspector general will "investigate allegations that funds are being improperly solicited by DCAA management officials from its employes" to finance legal costs of Starrett and the two demoted officials. He declined further comment.

Bickel, in his letter, said he was "a little disappointed" that only $6,300 had been raised. He listed contributions by each of DCAA's six regional offices, headquarters, the agency's training facility in Memphis, retirees and the special group that audits classified weapons contracts.

"Now, we ought to be able to do better than this," he wrote. "We are a long way from any goals we may have set -- so now is the time for some publicity and personal salesmanship.

"We need your help, and I know three special people who can use this money -- don't forget them."