The Supreme Court yesterday let stand a lower court ruling that Arlington's now-abandoned policy of strip-searching all persons admitted to the county jail was an unconstitutional violation of privacy.

The ruling resulted from the case of Northern Virginia attorney Lucy N. Logan, who was arrested on drunken driving charges in March 1979. When she refused an alcohol breath test, a magistrate ordered her jailed. At that time, policy set by then Sheriff J. Elwood Clements required all persons admitted to the jail to be stripped and searched for weapons or drugs.

Logan, who was eventually cleared of the charges, was searched by a jail matron.

Logan then sued county officials in U. S. District Court in Alexandria. Judge Oren R. Lewis dismissed the suit and denied her request for a permanent injunction against the strip-search policy, but the 4th Circuit Court of Appeals ruled last October that the search of Logan was unconstitutional and "bore no discernible relationship to security needs."

On appeal, the Supreme Court, without comment, left intact a ruling that such "indiscriminate search policy . . . cannot be constitutionally justified."

In 1980 alone, more than 4,500 people were strip-searched in Arlington following arrest on charges as minor as playing a stereo too loudly or eating a sandwich on the subway. After intense political pressure generated by publicity, lawsuits and public criticism, the policy of strip-searching all persons admitted to the county jail was abandoned in December 1980 by Sheriff James A. Gondles, who was elected in November 1979.