The Supreme Court yesterday sent to Virginia state courts a case challenging state rules that give lawyers amonopoly on the lucrative business of searching land titles in Virginia.

Without comment, the court refused to consider an appeal from a 4th U.S. Circuit Court ruling that stopped a U.S. judge from allowing nonlawyers to guarantee titles in Virginia.

In a controversial ruling. U.S. District Judge Robert R. Merhige had held that in April 1977 that the Virginia rules are "offensive to the notions of basic fairness," and violate federal antitrust lawyers.

Use of lawyers to search land titles in the state typically can add 1 per-cent to the cost of a home in the state and opponents of the practice had claimed that the use of nonlawyers would help lower home purchasing cost in the state.

In its ruling the appeals court said Merhige should have waited for a state court in Virginia Beach to have ruled on whether a title insurance company that used nonlawyers to handle its title worked had engaged in the unauthorized practice of law, State officials had brought charges against the firm contending that only lawyers can do title searches in Virginia.

"I'm certainly disappointed," said Alan B. Morrision, director of the Ralph Nader-founded Public Citizen Litigation Group that brought the suit on behalf of the insurance company. He said the group would have prefered for the case to remain in the U.S. courts.

"I'm comforted that at least we'll have the opportunity to bring the issue to conclusion in Virginia instead of in the Supreme Court," said Virginia State Bar President R. Harvey Chappell Jr.

According to affidavits filed in Merhige's opinion title insurance companies contend they could lower settlement costs by as much as $491 on a $60,000 home and $871 on a $100,000 home by using nonlawyers.