Eleanor Holmes Norton, head of the government's Equal Employment Opportunity Commission, has used a government-leased car to ferry her son, Johnny and two playmates from their Capitol Hill homes to the beauvoir Summer Camp in upper Northwest Washington.

Under federal law, U.S. officials, except for the president and Cabinet officers, are forbidden to use official government cars for private business or for travel from their homes to their jobs.

Norton, reached by telephone, conceded that she had used government cars to go back and forth to work and "occasionally" to take her child to the Beauvoir school, which she acknowledged "is not on my way to work." Her office is at 24th and E Streets, N.W. The school is near Washington Cathedral.

Norton said she had "not the slightest intention" of breaking the rules.

She said she had specifically asked an aide to check on permissible uses of the car when she took office. The aide, Terry Banks, said he had called the Justice Department Office of Legal Counsel and received a verbal advisory that "heads of . . . agencies [such as EEOC] are not limited by" the federal statue, even exempts only Cabinet members. He could not remember who gave him this opinion.

Official at the Office of Legal Counsel said they do not remember making any such statement, and one said, "I don't see how taking kids to school can be exempt."

An aide to Sen. William Proxmire (D-Wis.) said that on Feb. 18, 1977, before Mrs. Norton came to EEOC, the agency wrote Proxmire that it had determined that "no official is exempt" from the auto-use law at EEOC.

Federal law and General Service Administration regulations forbid government personnel - on pain of suspension for at least a month without pay - from using government vehicles for anything but "official purposes."

A GSA attorney said the use of a government car to take an official of a minor agency to and from work, or transport a car pool including an official's child to summer camp, "does not appear to be consistent with the rules governing the use of vehicles."