For the third in eight months, Arlington prosecutor William S. Burroughs has asked both a state judge and an arlington grand jury to convene a special grand jury to investigate possible misconduct by Virginia Attorney General J. Marshall Coleman and the state police.

Burroughs, a Democrat running for reelection in November, made his latestt request yesterday after a two-hour session with the county's regular grand jury. The grand jury deferred until Monday a decision on the prosecutor's request. Jury foreman Sherfy Jones told Circuit Court Judge Paul D. Brown that the panel wants to hear additional testimony from a member of the Virginia State Crime Commission.

Last July the commission issued a report mildly critical of some practices of the state police investigations division, which in 1978 at Coleman's request conducted a probe of Burroughs' handing of celebrated 1977 double -murder case. That three-month investigation cleared Burroughs of criminal miscounduct charges.

In his instructions to the jury yesterday, Judge Brown remined the panel that under state law, a special or investigative grand jury cannot return indictments but can only issue a reports.

"A special grand jury is quite expensive," Brown added, telling the jurors that on Monday he would ask them only one question: whether they wanted to serve on a special grand jury.

Twice in the last year Burroughs has been rebuffed by two other county Circuit Court judges, Charles S. Russell and Charles H. Duff, both of whom refused Burrough's request to appoint a special grand jury after a majority of jurors declined to serve on the special panel.

In Richmond yesterday, Coleman, a Republican who has called Burroughs' allegations "nonesense," said, "It's unfortunate that Mr. Burroughs is continuing his efforts to use the judicial system for his own personal ends."

Burroughs' opponent in the Nov. 6 general election, Republican-backed Henry E. Hudson, declined comment until after Monday's hearing.