They call themselves "the thin blue line" and since the 1950s their crime-fighting exploits have been the staple of nightly television melodramas. In shows such as "Dragnet," "Adam-12" and "Police Story" the self-image of the Los Angeles Police Department has poured over millions of screens - an image of a law enforcement group totally incorruptible and dedicated to duty.

Beyond winning the hearts of the masses of television viewers, the Los Angeles Police Department has also won the respect and admiratio around the nation of law enforcement officers from beat cop to police chief as one of the nation's toughest, most efficient crime-fighting organizations.

"Its honesty and integrity are unquestioned," said one enthusiastic LAPD booster, Willie Bauer, for 17 years chief of the Beaumont, Tex. Police Department. "Its professionalism is truly outstanding. I've seen their training and administration and was deeply impressed.

But in recent months the LAPD's stature has been undermined by a series of lawsuits and investigations mounted against the department.

Among the more serious have been:

An investigation by the Los Angeles district attorney's office into the recent fatal police shooting of an unarmed naked, white biochemist that has led to charges by minority groups that other killings by police of blacks and hispanics have never been similarly examined.

A joint probe by the district attorney and the state attorney general into the possible unlawful shredding of 25 years' worth of citizen conplaints against the LAP.

Federal and individual citizens' suits charging the LAPD with such severe discriminatio that the most recent statistics (up to the middle of 1976) show the number of women officers in the department decreasing.

All these cased could have statewide political significance after January when Police Chief Edward M. Davis steps down after eight years. He is widely expected to run from the Republican nominiation for governor. In the primary, Davis' main opponent now would appear to be state Attorney General Evelle Younger, whose department is investigating Davis and his police force for possible unlawful conduct in the shredding case.

Many observers here believe the LAPD's image has been most tarnished by the pre-dawn shooting Aug. 4 of Ronald Kieth Burkholder, a 35-year-old biochemist, in front of his laboratory. The officer involved, Sgt. Kurt Barz, claims the wiry, 5-foot-9 scientist was climbing up a street sign post nude when the officer spotted, him. Barz them claims Burkholder ran toward him, and knocked his nightstick out of his hand twice by the use of judo techniques. Only then, Barz claims, did he draw his pistol and shoot him six times.

LAPD's version of the Burkholder shooting has been treated with widespread skepticism. District Attorney John Van de Kamp, often mentioned around here as a possible candidate for FBI director, has ordered a full-scale investigation into the shooting. In addition, a $1.25 million civil suit against the city has been filed by attorney Stan Arnold on behalf of Burkholder's infant daughter, Isis Sari, who was born less than three weeks after her father's death.

Arnold seeks to prove that Barz shot Burkholder unnecessarily. "I'm a Republican and I've always been for the police, but the way this was handled was abominable," Arnold said. "We give the police weapons because they have our confidence. We are like little babies in their arms. But this policeman has brokent that confidence."

Davis, meanwhile, appears convinced Barz will be vindicated and blames the news media for building up the case. "[A] witness has now been found and he sustains the position of the sergeant," says Davis.

District Attorney Van de Kamp, who found the new witness, due to testify at the scheduled Jan. 17 inquest on the Burkholder shooting, chided the 60-year-old chief. "I would like to wait and see if I were Ed Davis," said Jan de Kamp.

The furor over the Burkholder hearing has injected new life into efforts by local liberal, black and Hispanic groups to reform the Los Angeles Police Department's shooting policy.

Michael Zinsun, the chairperson of Watts' Coalition Against Police Abuse, believes the Burkholder shooting has made whites aware of what he call abusive police practices that previously, have been restricted to Los Angeles' large black and Hispanic communities.

"This shows very clearly what has been happening in the black and brown communities here says Zinsun, whose group runs a private police complaint bureau. "We have scores of cases where black people have been shot down but nothing has happened. But it may change now that it's happened to a white, middle-class person."

The concern over the Burkholder and other police shootings had led to new, unprecedented political attempts to curb the police department's policy.

This September, six weeks after the Burkholder killing, the usually pliant civilian Police Commission here changed the LAPD's firearms policies.

In the past officers were allowed to shoot any fleeting suspect who the officer had reasonable cause to believe had committee a violent crime. Now officers can fire only when the fleeing suspect is known to have both committed a violent crime and remains a threat to others.

Davis was left fuming about the firearms policy, but meanwhile, a potentially more damaging development is the joint probe being conducted by the Los Angeles district attorney and the state attorney general into charges the LAPD may have unlawfully destroyed records of some 25 years of citizens complaints.

Intradepartment correspondence of the LAPD indicates the police first decided to shred the files, covering nearly 25 years of unsustained complaints against police officers, after a series of court decisions indicated the police would have to surrender those files on request from defense attorneys. The "adverse effect on the morale of police officers" the files were having, the internal reports said, was a prime reason for the shredding proposal.

Counseled by the Los Angeles city attorney's office, headed by Burt Pines, the LAPD went to the City Council in May, 1976, and asked for permission to destroy what were described as "internal affairs miscellaneous records." The council granted it virtually without debate and over the next two days over four tons of documents were shredded.

"We were told it was just odds and ends, little things not worth bothering with," said city councilman Zev Yaroslavsky.

Since the shredding took place, several local judges have denounced it was improper and scores of criminal cases have been thrown out of the court because the shredded files often requested by defense attorneys cannot be produced for discovery.

The case against shredding has been bolstered by records made public by Stan Levy, a lawyer now in private practice, who protested the decision when he was an upper-echelon member of the city attorney's office. "There was a deliberate decision by both LAPD and the city attorney's office. The police in power had the arrogance to feel they would do anything they wanted with their own files," he said.

Deputy District Attorney Don Eastman, who has been directing the shredding probe since it started in June, says between 25 and 30 people in the city attorney's office and the LAPD are being investigated for their role in the affairs. He says the possible charges include obstruction of justice and perjury. "The chief is being considered by the investigation as well as the city attorney," Eastman said. "It is a touchy case and painful to do."

But sources close to the investigation say neither Davis nor Pines will be reached by the investigations.

District Attorney Van de Kamp denies, however, that any assurances have been given to the chief or Pinces, himself a probable candidate for the Democratic attorney general nomination. "There have been no assurances given to anyone in the higher level," Van de Kamp said. "I've never talked to the chief about this personally at any time.

Davis, who says his role in the shredding consisted of one "twenty-second" conversation with an assistant chief, fings nothing wrong in his department being investigated by the office of his probably GOP gubernatorial primary opponent. "We did absolutely nothing wrong and if we did, you can bet your boots it would have come out by now," Davis said.

Davis' department has weathered other probes and other suits in recent months. Earlier this year a Justice Department suit charging the LAPD will sexual and racial discrimination in hiring was stopped by an injunction from a federal district court. According to Justice Department lawyer Mark Gross, the case could cost the LAPD over $3 million a year in enforcement assistance administration funds if successful on appeal, later this winter.

Another key discrimination case, filed by a former LAPD woman police sergeant, Franchon Blake, has also been rejected in federal court and awaits an appeal later this winter.

Blake charges that Davis, by imposing such "unisex" standards as a five-foot-six-inch height minimum for women, allowed the number of women officers to drop in his first five years as chief from 1978 to 152, or slightly over 2 percent of the department of 7,000 officers. Blake contends this took place when police departments around the country were drastically increasing the number of women on their forces.

Despite the range of charges against the department Davis and his supporters believe the department's image remains pristine.

Davis points proudly to last year's nearly 2 per cent drop in Los Angeles crime rate, and claims an eight-year drop of 40 per cent in crime in the black Watts section is evidence that his hard-hitting, no-nonsense approach works.

The Chief is confident that his department's tough attacks on such so-called victimless crimes as prostitution and marijuana smoking have all contributed to these impressive crime figures.

He hopes to share his thoughts on crime with the reading public in an upcoming book, "Staff One," this winter. Another book, titled "Hang Them at the Airport," a reference to the chief's famous prescription for dealing with airplane hijackers, will follow.