One day last January, the Bethesda-Chevy Chase Rescue Squad was giving oxygen to a 90-year-old Northwest woman who had inhaled smoke from a burning pan at her home four blocks inside the District.

A D.C. Fire Department ambulance arrived, according to the woman who called for help. Its crew ordered the rescue squad crew to stop treating the patient and refused to let them transport her to Sibley Hosptial, as she requested.

On July 5, D.C. Fire Department medics sped to an auto accident on Dalecarlia Parkway in Northwest, but found two ambulances, a rescue squad and a chief's car from the Bethesda-Chevy Chase company already there. The D.C. crew, in a written complaint to their superiors, reported that "tempers flared" and the rescue squad crews "blocked" them from the patient, who was treated by the Bethesda crew.

These disputes are part of an escalating feud over whether the suburban rescue squad can operate in the affluent neighborhoods of Northwest Washington, west of Rock Creek Park.

According to officials on both sides, such encounters occur often in Northwest between the D.C. Fire Department, which has the nation's busiest ambulance fleet, and the Bethesda squad, which is based 1 1/2 miles outside the city at 5020 Battery La. and has been providing free ambulance service to that part of the city since 1938.

Both sides say patient care is their primary concern and insist they want a peaceful resolution to the problem, but each charges the other with endangering lives and fueling tensions.

In March, D.C. Fire Chief Theodore R. Coleman, faced with complaints from his firefighters and ambulance drivers, ordered the Bethesda rescue squad to keep its ambulances outside the District unless called in by the fire department.

"They have completely ignored our policy, and I'm not going to tolerate that at all," Coleman said.

Rescue squad officials acknowledge they are defying the District policy. Rescue squad deputy chief J.S. Vayer said his squad accepts the fire department's authority to regulate emergency services in the District, but he added it cannot exclude a private ambulance company from answering requests for service from city residents.

Last year, about 2,500 of the rescue squad's 11,000 calls were in the District, Vayer said.

Chief David S. Dwyer, head of the rescue squad, said his crews only respond to calls in the District when they are telephoned by residents or witnesses to an accident. The squad once responded to emergencies broadcast on the D.C. police radio, which they still monitor, but Dwyer said that practice has been discontinued.

"We've been handling emergency calls in the District for 40 years, and we've done a damn good job," Vayer said. "After 40 years, you can't end a service without notifying the people who have come to depend on it."

The fire department charges patients either $55 or $70 a call, depending on the level of care. The rescue squad's services are free, funded by its annual door-to-door charity drive. A spokesman for the Bethesda squad, a nonprofit corporation, said $100,000 is raised yearly in the high-income area of the District it serves.

Vayer said ceasing operations within the District could cost the rescue squad $100,000, about one-fifth its budget, and its ability to assist the D.C. Fire Department if needed.

"It's up to us to determine the level of care needed in every case," said Battalion Chief Michael Tippett, a department spokesman.

"We're not going to back off. . . . We don't want to get nasty, but we'll do anything appropriate to resolve this," Tippett said.

Rescue squad officials said city fire dispatchers frequently call off rescue squad crews even though they are closer to an emergency scene than the city's own ambulances and that they sometimes refuse to let them treat or transport patients, regardless of the patient's wishes.

District officials counter that the rescue squad, in order to allow its crews to reach the scene first, is slow to notify the fire department when it gets a call in the District.

Because the two services do not coordinate their travel routes, fire department officials said, their ambulances sometimes nearly collide.

The rescue squad denies that it delays notifying the fire department: "It's an absolute falsehood. We've been listening to that stuff for over five years. It's absolutely not being done," Vayer said. He said the fire department has never been able to prove the allegation.

But fire department officials, the union representing city firefighters and individual firefighters have compiled reports that they say document two to three "run-ins" a day with the rescue squad, according to fire department Capt. James Misenheimer of Engine Co. 31. He said most are instances where Bethesda crews arrived at emergencies before D.C. crews.

One written complaint filed with city fire officials by Misenheimer blamed an alleged delay in notification by the rescue squad for a death on April 10, 1980.

Misenheimer wrote in the report to his superiors that Engine Co. 31 got a call from the rescue squad that it was responding to an emergency on Belt Road NW, just inside the city. Engine 31 immediately dispatched its rescue team to the scene, where a man was reported to be having trouble breathing, Misenheimer wrote. He said the patient might have lived if they had been notified three minutes earlier.

Misenheimer said the rescue squad's ambulance arrived from Bethesda at the same time as the District team. That would have been impossible unless they had a head start, he said.

Vayer disagreed vehemently with Misenheimer's conclusion. He said if there was a delay in dispatching the District unit, it was the fault of the District's dispatchers.

Vayer said the rescue squad crew could have reached the scene about as quickly as the District ambulance.

Vayer said that if anything reduced the patient's chances of survival, it was a District policy that prohibited a rescue squad mobile intensive-care unit from entering the city. The patient had to be transported several blocks by the Bethesda ambulance and transferred to the mobile ICU, which was waiting just across the line.

D.C. fire officials said the rescue squad's services in the District have become increasingly unnecessary as their department has grown over the years to a workforce of 1,664, including 193 emergency medical personnel, with an annual budget of $50 million.

Tippett said the the rescue squad is "like an unwanted house guest." Its operations make it difficult for the District to justify adding the equipment and personnel needed to serve the entire Northwest area. The rescue squad has created a "huge morale problem," said Bill Mould, president of the union representing the city's 12,000 firefighters.

Until recent years, there were no city ambulances or rescue squads stationed in the area served by the Bethesda rescue squad. A rescue team was placed at 4930 Connecticut Ave. in l976. Eighteen months ago, a full-time ambulance was placed at 4300 Wisconsin Ave.

According to Firehouse, a magazine for firefighters, the District's corps of public ambulances in 1982 was the busiest in the nation, with 17 ambulances running a total of 90,000 calls.

The D.C. ambulances are in almost perpetual use, providing emergency care within the city's 69 square miles, where the population swells each workday from 630,000 to almost 1 million, not counting 15 million tourists each year.

Response time for basic life-support ambulances, which are the workhorses of the fleet, average about eight minutes, or twice the national standard.

Sterling W. Hackett, 58, owner of a private Northwest company, Emergency Ambulance Service, who is familiar with the ambulance squabble, said he thinks the Bethesda rescue squad is overly selective in its service area.

"They have beautiful equipment and a wonderful reputation, but they're as wrong as two left shoes," Hackett said. "They don't serve the entire city, they serve the section where the money is, and that's why there's so much resentment. You won't catch them answering calls down in the Shaw area."

Vayer said, however, his service area is based on the number of calls, limits on their resources and perceived need. He said if the Bethesda rescue squad gets a call from beyond its normal range in the city, it will notify the fire department and will respond if the department requests help.