Arlington prosecutor William S. Burroughs Jr. went before a rare closed meeting of a Virginia legislative committee today to complain about how State Attorney General J. Marshall Coleman ordered a state police investigation of Burroughs' handling of a celebrated murder case.

Burroughs was joined by another prosecutor and a sheriff in protesting to the House Courts of Justice Committee how police investigated them.

In an interview after the closed meeting, Burroughs said he complained to the legislators that he was unfairly stigmatized and kept in the dark about the probe. "I couldn't find out what I was supposed to have done wrong," Burroughs said.

"I was eventually exonerated, but it took me four months to establish that there wasn't anything to find out," he said.

Burroughs said he is still trying to track down the source of allegations that he mishandled the investigation into the murders of Alan W. Foreman, 26, and Donna Shoemaker, 25, whose bodies were found inside Foreman's yellow Jaguar on May 8, 1977.

House Majority Leader A. L. Philpott (D-Henry), who serves on the House committee and is a former Henry County prosecutor, said later today that it was too late in the session to legislate guidelines for such investigations. But he said the committee might try to suggest some interim procedures for the police.

"This is a serious matter," said Philpott, who is a member of a special subcommittee of the State Crime Commission that has been examining the issue. "You can't imagine what it would be like to wake up in the morning and read in the newspaper that you're being investigated."

Yet that, according to Philpott, is exactly what Burroughs, a Patrick County prosecutor and a Dinwiddie County sheriff claimed had happened to them in testimony they each gave the committee today.

'It's a question of whether or not a public official should be advised," said Philpott, who stressed that Virginia law prohibits the attorney general and the state police from launching investigations unless they cite a specific charge.

"And they just refused to tell them what the charge is," Philpott said. The legislative committee intends to discuss the problem and, at the least, might write a letter to the state police objecting to their procedures, Philpott said.

Coleman issued a statement late in the day that defended his and the state police's investigating methods but failed to focus on specific compaints by Burroughs and Philpott.

"The purpose of a state police investigation of alleged criminal conduct is to establish grounds for legal action or to lay the allegations to rest," said Coleman. He argued that, "if anything, the attorney general's authority in this area should be increased.'

"As I have pointed out in my call for a statewide grand jury," Coleman said, "we need to provide more tools for the successful prosecution of crime. I assume the General Assembly will not want to muzzle the attorney general in the fight against crime or to cover up evidence of wrongdoing."

Noting that the state police investigations in question had all been ordered at the request of commonwealth attorneys or law enforcement officials, Coleman said such probes are 'the only means the commonwealth has to protect the people of Virginia from abuse of power by local elected officials."

The attorney general has the power to order state police investigations if requested to do so by local authorities. Such a probe of Burroughs was ordered by Coleman in April 1978 following complaints by Arlington County police and a few citizens that Burroughs was failing to pursue the county police investigation of the Forman-Shoemaker murders.

Although Burroughs complained today that none of those interviewed by state police made allegations against him, the investigation continued until mid-July when Coleman said he could find no wrongdoing on Burroughs' part and closed the case.