Thirteen people died during a 16-day period last month in the District from injecting themselves with a potent mixture of cocaine and the painkiller Dilaudid, according to police and public health officials, who also predicted that 1987 would set a record for drug overdose deaths here.

The Dilaudid deaths, combined with 14 others from heroin or cocaine last month, brought this year's death toll to 143 -- just one short of the total number of fatal overdoses during all of last year. Alarmed officials said they now believe this year's total will exceed the record high of 155 deaths set in 1985. Some predicted it would exceed 200.

The increase in overdoses, along with record numbers of drug arrests, drug-related homicides and emergency room visits, reflects the city's worst drug-use epidemic ever, authorities said.

Use of all drugs is most prevalent among young black men, they said, and the biggest killer by far is heroin. "If you live in a world where you think you have a better chance to go to jail than to college, then you make your life-ending decisions in a perspective that is already bleak and hopeless," said Dr. Reed V. Tuckson, D.C. public health commissioner.

"We're going to have to find ways to reach out to the population that is abusing drugs and offer them a sense that there is a future, that life has more to offer than the transient happiness of the abuse of drugs," Tuckson continued. "You have to have treatment facilities. You can't as a city continue to say, 'Not in my neighborhood,' because as long as you do, people are going to continue to die."

Nationally, experts say that drug use appears to have peaked among educated, affluent Americans, after a period of widespread acceptance in the '60s, '70s and early '80s. But they note that use of dangerous drugs such as cocaine and its more potent form, crack, is increasing, especially among poor Americans. From 1982 to 1986, for example, the number of deaths and emergency room reports involving cocaine quadrupled nationwide.

The last reported Dilaudid death here occurred Sept. 16, according to the D.C. medical examiner's office. Dilaudid is a morphine derivative used to relieve pain in terminal cancer patients. Eight times more potent than morphine, it is coveted by street addicts as a substitute for heroin. Until September, Dilaudid overdose deaths were rare in the District because addicts normally bought small doses of the drug in pill form.

Authorities speculated that the recent overdoses were caused by someone in the city passing off Dilaudid in powdered form as heroin.

Because of the District's Dilaudid deaths, the federal Drug Enforcement Administration has issued a national alert for thefts of Dilaudid and has begun a detailed, regional audit of supplies of the drug, according to an agency spokesman.

D.C. police also are investigating the source of the killer drug that is known on the streets as "White Man's Heroin," "Juice," "Dillies" or "D's."

"What happens is legitimate handlers of Dilaudid like doctors, pharmacies and hospices will have someone backdooring the drug," said special agent Bob O'Leary, spokesman for DEA. "We also want to make sure we don't interrupt the flow . . . to the people who need it because people for whom Dilaudid is prescribed are in desperate pain."

Police attributed the general upsurge in drug overdose deaths in recent years partly to a startling increase in the purity of drugs available on D.C. streets. The increasing purity has paralleled a nine-year increase in drug overdose deaths, which soared from a low of seven in 1978 to an all-time high of 155 citywide in 1985.

For example, the average purity of heroin available on the streets of Washington increased from 1.8 percent in 1978 to nearly 11 percent this year, according to police. Because heroin is so abundant, dealers must lower prices to be competitive or increase the purity to move their product, police said.

"Since there is higher quality stuff out there, it's only natural that there would be more overdose deaths," said Capt. Larry Soulsby, commander of the D.C. police department's homicide squad. "Eventually someone is going to take a little too much or mix it with alcohol. But I don't think anyone wakes up and says, 'I want to die today, I think I'll get drunk and take some heroin.' "

There have been 143 drug overdose deaths reported already from the beginning of this year through September, city officials said. That toll includes the death of 15 addicts -- two in July and 13 in the first 16 days in September -- from the Dilaudid and cocaine mixture. A total of 27 people took fatal overdoses in September and 30 died of overdoses in July, making it the city's most lethal month ever for overdoses.

"That's about one a day in those two months. Normal is 125 to 140 {overdose deaths} all year. This year if things continue, we'll probably see over 200 deaths from drug overdoses," said Philip Santinga, senior toxicologist in the D.C. medical examiner's office.

There are other signs of the District's drug epidemic. More than 60 percent of the 161 homicides in the city this year have been drug-related, police said, a marked increase over last year when about one-third of the murders in the city were drug-related.

From 1982 to 1986, felony drug arrests rose 177 percent, felony drug prosecutions soared 509 percent and felony drug convictions increased 559 percent, according to a recent study by the D.C. Office of Criminal Justice Plans and Analysis. The study also found that last year, nearly 70 percent of adults arrested in the District tested positive for one or more drugs.

Emergency room treatment for drug abuse soared between 1982 and 1986, according to the study, rising 293 percent for cocaine and 445 percent for PCP, a hallucinogen that frequently makes users violent.

Isaac Fulwood Jr., assistant D.C. police chief for field operations, noted that the statistics tell only a fragment of the story. "You have to look at the human side," he said. "I wish I could paint a picture of this person who's 25 or 30, primarily black male. They may be addicted to drugs, but they're still human.

"When you get {a prediction of} 200 overdose deaths, how many families did that affect? How many friends were left behind?

"It's murder. The person who sells another person a controlled substance should be charged with murder."