The numbers were remarkable even for a city in Kentucky, which is one of the top five states in the nation for overdose deaths.

In a span of 32 hours last week, emergency workers in Louisville responded to almost two calls per hour for overdose patients, the highest rate so far this year. Only one person died, but officials said on Monday that the number raised concerns that drug-related overdoses and deaths, which started rising last year, are accelerating.

Mitchell Burmeister, a spokesman for the Louisville emergency medical services, did not have a breakdown of what caused the overdoses, whether it was heroin, alcohol or some other drug, even prescription drugs.

Still, Mr. Burmeister said the number of calls in last week’s spike between early Feb. 9 through the next morning on Feb. 10 was the biggest so far this year. It compared with 25 such calls in the same period the week before. The annual figure for overdose calls was 6,879 in 2016, up from 4,642 in 2015, Mr. Burmeister said.

“We put out an advisory to our crews that it was a little bit higher than normal, and we are trying to make sure that there is nothing more systematic,” he said in a telephone interview on Monday.

“It ebbs and flows,” he said, adding “it’s fair to describe that as a spike.”

With a population of about 590,000, Louisville is the largest city in Jefferson County, which had the greatest number of deaths in the state from heroin, or 131 in 2015, according to state figures.

Kentucky is one of the five states with the highest rates of death linked to drug overdose: West Virginia (41.5 per 100,000), New Hampshire (34.3 per 100,000), Kentucky (29.9 per 100,000), Ohio (29.9 per 100,000), and Rhode Island (28.2 per 100,000), according to the Centers for Disease Control and Prevention.

Less than half of the emergency call patients, or 18 of them, received Narcan, an opiate antidote, said Mr. Burmeister.

Steve Moran, a deputy coroner, said the coroner’s office could not confirm that the one death out of the 52 overdose emergency calls last week was caused by a heroin overdose until they receive a toxicology result.

Kentucky is not alone in coming to grips with what a nationwide trend in the rise of opioid abuses and related deaths. The state has partnered with the federal Drug Enforcement Administration’s 360 Strategy program, which includes community outreach and law enforcement efforts to combat trafficking, Mr. Burmeister said, and it is also reaching out to officials in other areas of the country where opioid abuse has had a significant impact.

Over the past 10 years, the drug landscape in the United States has shifted, with the abuse of controlled prescription drugs, fentanyl and heroin having “risen to epidemic levels,” the D.E.A.’s National Drug Threat Assessment survey of 2016 says.

Drug overdoses have become the leading cause of injury deaths in the United States, it says. Every year since 2009, drug poisoning deaths have outnumbered those by firearms, vehicle crashes, suicide and homicide. In 2014, approximately 129 people died every day as a result of drug poisoning, the report said.

Timothy J. Plancon, a D.E.A. special agent in charge of Ohio, Michigan and Kentucky, said that the Kentucky calls fit a pattern of high numbers of overdoses related to opioids that officials are seeing in those three states.

”Multiple overdoses related to fentanyl abuse and other opioid abuse spiked in the middle of 2016,” he said. “And it seems to keep getting worse.”

The C.D.C. says that 91 people in the United States die every day from opioid overdose.

Mr. Moran said in his two dozen years as a law enforcement officer and at the deputy coroner’s office, he has never seen so many heroin-related overdose deaths, which have multiplied to several a week or about one a day at the highest, compared with about one a month in the past year.

“Here locally, people are shooting up in hospital parking lots in case they overdose,” he said. “Some have already overdosed two or three times prior to dying, but they had Narcan administered and they survived.

“It is Russian roulette, is what they are playing,” said Mr. Moran.