You start with cocaine. You throw in the king of rock-and-roll, the scion of one of the nation's leading publishing families, Denver's police chief, Colorado's top narcotics officer and assorted other political and police figures, and you end up with a richly complex scandal that has tarnished many of the elements of this city's small establishment.

At the center of the tangled tale is Michael Balfe Howard, an heir to the Scripps-Howard newspaper fortune and former editor of the chain's Denver daily, the Rocky Mountain News. During the latter half of the 1970s, Howard's life was a delicate balance of cocaine and cops; he was addicted to the former while a close friend of the latter. He managed to live outside the law with impunity.

Howard was fired from the family paper in September, 1980, when his drug problem became overwhelming; he is currently undergoing treatment, and was unavailable for comment. The scandal surrounding him is just coming out now because Howard has been spilling the sordid details to The Denver Post, archrival of the paper his family owns.

The Denver Post, purchased last year by the Times Mirror Co., which owns the Los Angeles Times, is in the last weeks of a transition from afternoon to morning delivery. By mid-June it will compete head-to-head with the Rocky Mountain News, a morning tabloid. Battling hip and thigh for readership, the Post has used the Howard revelations as a key weapon in its war against Howard's old paper.

As spun out in the papers--and before a state Senate committee that had launched its own investigation--the Mike Howard saga has a familiar plot: a rich and successful young man is dragged down by drugs and pulls his friends down with him.

Howard's years at the Rocky Mountain News were successful. The tabloid became the region's best-read newspaper, a position it clings to today. Howard became friendly with virtually all the VIPs here--including some very important policemen.

When Howard was admitted to a hospital for treatment, Police Chief Arthur G. Dill brought ice cream to cheer him up (the chief says he thought Howard's problem was alcohol, not cocaine). When Howard dined on at least one occasion at a popular police hangout, his companions included the city's chief narcotics detective and the head of the Colorado Bureau of Investigation.

As the editor's drug problem grew more serious--he says he was spending $6,000 per week on cocaine in the late '70s--he tried to see that his important friends kept him out of trouble.

Howard became a patient of Dr. Gerald Starkey, the police medical coordinator and a specialist in drug abuse. Starkey says the doctor-patient privilege forced him to keep silent about Howard's addiction.

In his more daring ploy, Howard attempted to co-opt detective Ron Pietrafeso, the chief drug investigator for the state crime strike force.

Howard gave Pietrafeso $5,500 in gifts, and paid him $200 per month to serve as a "personal bodyguard," according to testimony before the Colorado Senate Judiciary Committee.

The drug investigator says he guarded the addict for 15 hours per week for two years but never noticed a sign of drug use. Pietrafeso said that when he did discover Howard's addiction, he immediately broke off relations.

In testimony before the state Senate investigators, police officials say they cannot remember many of the five-year-old details of their dealings with Howard. They say the relationship was based on honest friendship.

Howard, however, told The Denver Post that he was actively trying to buy protection. "I figured I was purchasing immunity," Howard told the paper. "I'm no . . . dope."

Testimony before the state Senate committee indicates that Howard's network of important friends helped keep him out of legal trouble. Despite increasingly open cocaine use, he was never charged with any drug offense.

At one Howard dinner party attended by the police chief, the Colorado Bureau of Investigation director, and top city and state narcotics police, the editor snorted cocaine and offered to share it with two law enforcement officials, according to testimony. No charges were brought.

Asked why in an interview this week, Police Chief Dill replied, "That's a good question."

Twice during his drug-ravaged years, Howard was charged with menacing a person with a loaded gun and flourishing the weapon. The first time, he won his innocence after proving that he had the police chief's personal authorization to carry the weapon. The second time, a friend of Howard's called the victim's boss in an apparent effort to stop prosecution. (The friend says he was just trying to find the victim's phone number.) Howard was convicted of flourishing the weapon in that case and served a year's probation.

The state Senate committee investigating all this has learned that Howard was not the only rich and prominent addict who had important friends here.

During five or more visits to Denver in the years before he died of a drug overdose, the committee learned that singer Elvis Presley became friendly with many of the same officers who were Howard's pals:

Presley gave Chief Dill a gun; he treated Pietrafeso, the drug investigator, and another police official to a free jet ride and stay at his mansion in Memphis. In an orgy of generosity one night in 1976, the singer gave brand new luxury cars to at least four police officials here.

At one time, Presley, a police buff, was given state and city police credentials. Police Chief Dill bought the singer a Denver police captain's uniform. Presley wore it to two police social functions and asked to go along, in uniform, on a real drug bust. There is conflicting testimony as to whether this request was granted.

The Denver police have told The Denver Post they had no inkling that their friend Presley was a drug abuser. "He was anti-drugs, as far as I was concerned," said Capt. Jerry Kennedy, chief of the vice and drug bureau.

Whether anything but embarrassment will flow from the Howard scandal and its Presley tributary remains unclear. There are several investigations going on now, but the dimming of memories and the statute of limitations may end the matter. Howard still faces a civil suit over his second gun incident. But that seems unlikely to produce anything more than additional headlines.

Propelled partly by its intrinsic fascination and partly by the newspaper war, the scandal has gained enormous attention here and prompted the predictable outburst of jokes and sarcasm.

When you look closely, though, the most striking feature of the Howard affair is its unremitting sleaziness.

The atmosphere was crystalized in state Senate hearings this week when Starkey, the police physician, was talking about his relationship with Presley.

The two had a professional as well as personal relationship, the doctor insisted. "I took an ingrown toenail off of Elvis," he said.

Later, Presley offered to buy the doctor a luxury car. "He wanted to give me a Rolls Royce and I told him I didn't want it," Starkey declared in pious tones.

A few seconds later, the police physician testified he turned down the Rolls because he really wanted a Lincoln Continental--which Presley promptly provided.