Police have released a sketch of a person of interest in connection with the shocking killing of a retired university dean who was shot in the head while walking on a Vermont trail last week.

Honoree Fleming, 77, was found dead on a trail on Oct. 5 in Castleton, Vermont State Police said. She died from a gunshot wound to the head. The medical examiner determined the manner of death was homicide, police said.

On Wednesday, police released a sketch of a person witnesses reported seeing on the trail prior to the discovery of Fleming's body.

Capt. Scott Dunlap, commander of the Vermont State Police Major Crime Unit, called it their "best lead" yet, as no suspects have been identified nearly a week after the deadly shooting.

"It's somebody that we want to talk to in regards to her death," Dunlap told reporters during a press briefing Wednesday.

More than one person saw the man on the trail, and the composite sketch was made based on their accounts, according to Dunlap.

"We've had witnesses that came across him acting very strangely, oddly," said Dunlap, who did not provide any additional details on the person's behavior.

The person of interest was described by witnesses as a white man in his 20s, approximately 5'10" with short red hair. He was last seen wearing a dark-colored T-shirt and carrying a black backpack, police said.

It is unclear if the killing was random or targeted, Dunlap said, urging the public to "remain vigilant."

Authorities asked residents to contact police if they recognize or believe they see the person of interest.

"Do not confront this person," Castleton Police Department Chief Peter said during the briefing. "Do not try to do anything on your own."

Fleming, who lived in the town, was out for her regular evening walk when she was shot, Dunlap said.

She was a retired dean of education and "beloved teacher" at Vermont State University Castleton Campus, the university said. She was the wife of Ro Powers, a Pulitzer Prize-winning journalist and New York Times bestselling author.

Vermont Gov. Phil Scott called her death "tragic."

"We are still trying to find out why. That's the piece that's missing," Scott told ABC Burlington affiliate WVNY on Tuesday. "I know our law enforcement is doing all they can to find any leads."

Scott said he knows residents are feeling frustrated and scared amid the investigation.

"We need a lead, we need something to go on," he said. "Our law enforcement team is working nonstop to try to find the killer who did this."