Attorney General J. Marshall Coleman has asked the State Supreme Court to order new hearings on whether a Northern Virginia woman can be prevented from taking the bar examination because she lives with a man who is not her husband.

The court recently agreed to hear an appeal of the case by Bonnie Cord, a U.S. Energy Department lawyer who lives in Linden, Va., and was denied the right to take the Virginia bar exam by Warren County Circuit Court Judge Duncan C. Gibb.

Gibb ruled that Cord's admitted living arrangement "would lower the public opinion of the bar" and refused to grant her the certificate of good character she must have to take the exam.

Coleman is required by law to defend Gibb's ruling on appeal, but he told the appellate court in a memorandum that he believes it will find that the Cord decision was based on an insufficient record before Gibb and the case will be returned to him for further hearings. He asked that the case be sent back now, before the appeal is heard.

Coleman said a new hearing should establish whether Cord actually has violated the state law against lewd and lascivious cohabitation, whether that law is enforced in the state, whether it can be used as a standard for moral character, whether the same standard should be used for bar admission and what statewide standards, if any, the Virginia State Bar or Board of Bar Examinesr applies in such cases.

Coleman said the mere admission by Cord that she lives in same house with a man who is not her husband did not establish a criminal violation. He argued that evidence of premarital sexual activity apparently is insufficient to bar someone from the legal profession and suggested that a new hearing before Gibb should try to establish whether Gibb Cord was guilty of a continuing violation of the law and maintains her right to do so.

Cord's lawyer, Thomas V. Monahan of Winchester, said in an interview that he has mailed an answer to the court opposing Coleman's motion and asking that the case be decided on constitutional grounds he raised in appealing the Gibb ruling.