he death of an elderly Alexandria woman, killed when the car in which she was riding was struck by a speeding police cruiser, illustrates what critics claim is a shadow on law enforcement; the hazard to civilians from police responding to emergencies.

Nationally, more than 500 people are killed each year after crashes with police driving to a crime scene or chasing a suspect, according to a study made 13 years ago but still believed accurate. Thousands more are injured annually, the study showed.

Consumer advocate Ralph Nader says those statistics mean that police officers in cars can be as dangerous as the criminals they are trying to stop.

"You're unleashing a missile when you let a policeman drive above the speed limit, yet no one does anything about it. Without public pressure, there is no reason for police department to change their policies."

An opposing view is voiced by former D.C. Police Chief Jerry V. Wilson. "Most high-speed chases do result in a catch of a suspected lawbreaker, said Wilson, now a vice president of the Peoples Drug Store Chain. "If you publicly announced police weren't going to speed, then every robber and hot-rod kid would know he could get away. Maybe those accidents are the price we pay for effective law enforcement."

In the recent Alexandria case, Officer Charles Daniel Keyes was driving his patrol car to the scene of a purse snatching Jan. 12 when the car hit a station wagon that was making a left turn from Rte. 1 on to Swann Avenue. Occupants of the station wagon were Everette M. Brewer and his wife, Mary Bibb Brewer, who were on their way to a dinner at a local Italian restaurant. The police car, which wasn't using its siren or flashing light, according to trial testimony, struck the vehicle on the passenger's side. Mrs. Brewer, 75, was killed.

Before Keyes' April 11 trial, a prosceutor said there was no evidence to support a charge more serious than speeding. A judge found Keyes guilty of speeding 60 miles an hour in a 35 mile zone and fined him $50.

Keyes, a member of the Alexandria force for two years, still could face police disciplinary action for failing to use his emergency warning equipment while driving above the speed limit. Brewer's estate has filed a $500,000 damage suit against Keyes and the city of Alexandria.

Keyes has declined all comment. His attorney said the officer feels "terrible, just terrible" about the accident.

In other Washington area accidents:

Al Biscoe, a National Science Foundation financial expert, was taking a lunchtime stroll at the corner of 19th and E streets NW last Sept. 27 when a getaway car occupied by some Arlington bank robbers raced down E Street with police in high-speed pursuit and struck him. He lost both legs and has filed a $25 million damage suit against the Arlington government, the county's police force, the officer who was chasing the robbers through crowded D.C. streets, the D.C. government, whose officers joined the chase, the robbery suspects and the man whose car allegedly collided with the getaway car when it ran a red light, knocking it into biscoe.

Four Alexandria teen-agers allegedly stole a car on Easter Sunday, then drove at least 80 miles an hour trying to elude a policeman who spotted them. Their car crashed into a stone wall at S. Quaker Lane and Duke Street after failing to make a turn. One of its occupants, Kevin Johnson, 17, died later of his injuries.

The policeman involved in the latter incident, Stuart L. Estler, was following accepted practice in driving above the speed limit -- up to 80 miles an hour -- while using his emergency warning lights and other equipment, a police investigation concluded.

One of the few studies of the phenomenon of civilians being killed by police cars -- the one that found that more than 500 civilians are killed annually by such collisions -- was made in 1967 by the New Jersey-based Physicians for Automotive Safety at Nader's request.

In only one out of five of those fatal accidents was the police officer resonding to a serious violation, the report said.

Dr. Seymour Charles, head of the New Jersey group, said that "the figures on accidents involving civilians and police haven't changed any since 1967. If anything, they've gotten worse."

In 1976, the last year studied by the San Francisco-based Americans for Effective Law Enforcement, a police lobbying group, there were 2,778 lawsuits filed against police departments and their officers because of traffic accidents, a spokesman said.

"The number of such lawsuits has been increasing steadily since the 1976 survey," added Bob Reeder, an instructor at Northwestern University Traffic Institute. "But no one really know how often police drive above the speed limit without using their lights and sirens," he said.

Most state laws permit police to drive faster than the posted speed limits if they use their lights and sirens, officials said.

The lawsuits and the accidents that spawn them, cost police departments and the taxpayers who support them millions of dollars each year in legal fees, damage judgements, and lowered efficiency from injured personnel, Reeder said.

Alexandria officer Keyes was on disability leave for several weeks because of a knee injury suffered in the accident that fatally injured Brewer.

One of the few attempts to find out on a minute-by-minute basis what speeds are used by police is under way in the D.C. Police Department's 1st (downtown) District, which an official said has "traditionally had the highest accident rate in the department."

According to Sgt. Dave Seller, a sophisticated $500 Tac-O-Graph, which records a police car's speed, has been installed in each of the section's 21 cars. The device, known informally as an "Iron Sergeant," has in part been responsible for a 31 percent reduction in accidents during the past year, Sellers said.

"From my experience police officers drive faster than the posted speeds more often than they should." Seller said, "When we read the Tac-O-Graph's records and see that an officer has a pattern of fast driving, we counsel him. I think it's working."

According to Seller, the section had 44 accidents in 1973 and 34 in 1979, after the Iron Sergeant was placed in the cars.

The District has some of the tightest regulations governing the police driving in the area. "We have them report accidents a normal motorist might just say, "The heck with it,' and drive on," says a spokesman. "All it takes is a transfer of paint and it has to be reported." The reports go before a five-member accident review board which checks every accident and is authorized to dock bad drivers' pay.

Montgomery County Police Department last year for the first time required all of its 775 officers to begin taking refresher courses in driving skills, spokeman Phillip L. Caswell said. Those refresher courses accounted in large part for the reduction in accidents in 1979, he said.

A former Montgomery County police officer, Harold L. Kramer, was driving a cruiser in hot pursuit of a suspect in 1970 when the police car struck and killed a pedestrian. Kramer was absolved from police disciplinary measures in part because he had not been fully trained in police driving techniques, the county personnel board ruled in 1971. Two D.C. juries were unable to reach a verdict in the incident, in which Kramer was charged with negligent homicide.

Caswell said the fear of another "Kramer-type incident" led his department to begin the retraining program.

Sgt. Michael S. McCampbell, head of the Northern Virginia Criminal Justice Academy, which trains all new police officers in Northern Virginia, said the academy is studying the possiblitity of requiring refresher driving courses for officers.

"There's probably a need for that. The accident rate for police is a real problem." said Susan Mull, an official with the Northern Virginia Planning District Commission.

The average accident rate for civilians and police nationwide is about 26 accidents for each million miles of driving, according to National Safety Council spokesman Jack Hecht.

Alexandria police had 66 accidents per million miles. Falls Church police had 48, Arlington 46, and Fairfax County 32 accidents per million miles. Only tiny Fairfax City police had an accident rate lower than the national average, with 21 accidents per million miles, according to Mull.

D.C. police had 60 accidents per million miles last year, according to Seller.

Both Mull and Hecht said police rates for urban areas were expected to be higher than the national average, which includes driving rates in rural areas.

In Prince George's County, which keeps 800 police vehicles on the road at all times, Capt. Bill Say Sahaydak said, "We have about one accident a day. Most are fenderbenders, but that's still way too high."

Chasing a suspect in a car often seems as much a part of the job description as a badge and a gun, one veteran police officer said recently.

"They teach you at the academy to watch your speed, keep it down, but sometimes there's a need to go fast. When you do, our adrenaline really gets pumping, and if you're using your lights and sirens, you can almost fly there by yourself," he said.