NEW YORK — Detectives hunting for the person who strangled a runner in a secluded New York City marsh were encouraged after genetic material found beneath her fingernails, on her phone and on her neck resulted in a DNA profile of her probable attacker.

A month later, their optimism has waned.

The genetic fingerprint didn’t match any of the profiles from convicted criminals in the state’s Combined DNA Index System. A check against the FBI’s DNA database also came up empty.

So for now, investigators are relying on traditional investigative techniques to try to identity Karina Vetrano’s killer, while the DNA sample joins 56,530 others on file with the state that have been lifted from crime scenes but have so far not been linked to a person.

“I would bet that in at least half of (DNA) cases, they get a suspect from analysis and their job becomes easy,” said Dan Krane, a DNA expert at Wright State University in Dayton, Ohio. “But in the other half, they have to resort to old-fashioned detective work.”

Vetrano’s killing has been an object of tabloid fascination in New York ever since her father, a retired firefighter, discovered her badly beaten body in a marshy park not far from her home on Aug. 2. She normally ran a route through the area with her dad, but an injury kept him from joining her that evening.

Investigators have interviewed cyclists and runners who frequent the Spring Creek Park trails, combed through Vetrano’s personal life for clues and even checked shoplifting and panhandling reports at a nearby mall as part of the hunt for the killer. They have also been examining convicted sex offenders who were imprisoned before the state DNA database was established in 1996, according to the police.

In all, detectives have so far received 85 tips, none of which has led to a break in the case, officials said.

New York Police Department’s chief of detectives, Robert Boyce, acknowledged the unsuccessful DNA match in a briefing for reporters this week but said, “We’re working outside those limitations right now to identify that person.”

Getting such a match can oftentimes take years, according to experts.

To preserve a path to prosecution, district attorneys in many states, including Ohio, Arkansas, Delaware and New York, have made a practice of securing criminal indictments in rape cases of “John Doe” defendants, who have been identified only by their DNA profiles.

That legal strategy was devised to stop the clock on statutes of limitation for sex crimes, but it also points to the frequency of instances where investigators have DNA but no suspect.

State and federal authorities regularly run comparisons against DNA databases to see if there are new hits.

There is no statute of limitation on murder — but the lack of a DNA hit makes Vetrano’s case harder to solve.

“The bottom line is, unless there’s other evidence that we don’t know about, if it’s just DNA, they’re in trouble,” said Lawrence Kobilinsky, a DNA expert who chairs the science department at John Jay College for Criminal Justice. “They’re going to have to wait until this guy makes a mistake.”

On Wednesday, authorities released a sketch of a man seen in the neighborhood the day of the crime, though they stressed he was being sought as a potential witness, not a suspect.

Police have said they don’t believe Vetrano knew her assailant, though some detectives believe she may have had a stalker. Her parents have publicly pleaded for anyone with information to come forward.

A comprehensive search of surveillance footage in the Queens neighborhood abutting the park yielded no images of a man emerging from the wetlands on the day Vetrano died, forcing investigators to shift their attention to a nearby bike path, Boyce said.

“At this point we shifted our investigation into the bicycle path, where there is no video,” he said. “So now we have to rely on witness ID.”