On Jun. 5, Braniff Airways asked the Civil Aeronautics Board for an "emergency exemption" to provide a severely injured, improverished 15-year-old girl with free air transportation from Miami to Denver where she could get the specialized medical treatment she needed.

Peggy Petrocci was severely injured in an auto accident in November, suffering a broken neck with two completely crushed vertebrae, attorneys for Braniff told the CAB in their application. She was in the Mt. Sinai Hospital in Miami: paralyzed from the neck down.

Doctors from Denver's Craig Hospital who specialize in the treatment of injured victims like Peggy had visited her in the Miami hospital and said they could take her as a patient beginning Jan. 11; in Denver, they could provide her with the specialized form of theapy she needs and could fit her with braces they have developed, the CAB was told.

But Peggy's family didn't have any money to pay the air fare. Her parents are divorced and her mother had to quit her job at the Intecontinental Bank of Miami Beach to be with peggy around the clock at the hospital to provide her with the constant attention they couldn't afford to hire a nurse to perform. Peggy's mother and her other two children have been living off contributions provided by Mrs. Petroccio's former fellow employees at the bank and from money collected by St. Patrick's Parish, the family's church in Miami Beach.

The Craig Institute had agreed to absorb whatever cost Peggy's treatment involved over the above what would be available through a health and accident policy maintained by her father's place of employment.

Because airlines are prohibited from granting free transportation, Braniff asked for an exemption to render "a humanitarian service generally analogous" to but not included in the definition of "general epidemic, pestilence, or other calamitous visitation" in the Federal Aviation Act. The petition noted that the board has historically authorized free foreign air transportation for seriously ill or injured abroad who could receive care in the United States not available in their homeland and were unable to afford the air fare. The situation is similar, Braniff contended.

The application noted that taking into consideration its advance bookings, it could fly Peggy and her mother on jan. 11 without displacing regular-fare traffic.

On Friday, Jan. 14, three days after Braniff had hoped to fly Peggy to Denver, B. Howell Hill, an attorney with Arnold & Porter representing Braniff, submitted a letter to the board asking that its application for the emergency exemption be withdrawn. "A private contribution to pay for the transportation in question has been arranged, and authority to provide free transportation is no longer required," he said.

Yesterday, at 10 a.m., Peggy, her mother, and a nurse, were flown aboard Braniff Flight 176 from Miami to Denver.

The private doner was Harding l. Lawrence, Braniff's chairman of the board, president and chief executive officer. "Mr. Lawrence personally took an interest in this when he heard about this and decided to pay for it - hopefully quietly and anonymously," a company spokesman said yesterday.

The tab was $924 - for the four round-trip first-class tickets that were necessary: two for Peggy's stretcher, one for her mother and one for the accompanying nurse.

The company officially says the application was withdrawn because it decided it would rather not set a "precedent" so long as the air transportation could be taken care of quietly.

But other sources say it was clear from the brouhaha at the board that the application probably would not be granted, and certainly not in a timely fashion. Although the board never officially voted on the application, the board's bureau of economics had formally recomended that it not be granted on grounds that it could set a "precedent." If we had allowed it, the line would have gone around the block," said one board source. "We simply don't have the institutional capability to decide which cases are worthy and which aren't.

Says another: "Everyone was sympathetic; who could be against it?"