A 78-year-old fugitive who escaped into a vast New York forest after allegedly murdering his daughter-in-law nearly five years ago is believed to be alive and living under an alias, police sources told Fox News.

Eugene Palmer, of Stony Point, N.Y., is wanted in the Sept. 24, 2012, shooting death of his daughter-in-law, Tammy Palmer, in what authorities described as a "cold-blooded" and "premeditated" murder.

While Palmer's sons claim their father -- a severe diabetic -- died in the woods of Harriman State Park, which is in southeast New York State, authorities said they suspect he is living in another state based on a fresh tip.

"We have recently received new information that has led our investigation out of state," Detective Sgt. George Lutz of the Haverstraw Police Department told Fox News on Monday.

"With the assistance of federal and local authorities we are investigating this new information," Lutz said.

"We have no evidence whatsoever that would lead us to believe that Eugene Palmer is not alive," he said, noting, "I can't imagine him using his real name."

On an early September morning, Palmer waited for his 39-year-old daughter-in-law to place her two children on a school bus before shooting her three times with a bolt action shotgun as she walked up the driveway toward her home, police said.

Palmer, a retired part-time park ranger, then fled into Harriman State Park -- a 46,000-acre stretch of woodland filled with caves, root cellars and abandoned mine shafts that bordered the man's home, according to police.

Lutz said Palmer drove to his niece's home shortly after the alleged killing and confessed to the crime. He also left money with his sister to pay his taxes and told the woman to give him an hour before contacting authorities, according to Lutz.

Hours after the shooting, police found Palmer's abandoned pickup truck on an old fire road about a quarter mile into the park. An extensive manhunt ensued, using air and foot patrols as well as bloodhounds. A "hit" was detected by one of the dogs, leading police to a campsite within the park, but it remains unclear whether the scent belonged to Palmer.

The Haverstraw Police Department also requested assistance from state and federal law enforcement, including the FBI. They found no conclusive evidence of Palmer in the park, other than his truck parked deep into the woods. "He knows this park like the back of his hand," Lutz said of Palmer, known to locals as a so-called "Mountain Man," well-versed in the many trails and caves inside the park.

A law enforcement source previously told Fox News the U.S. Marshals service was assisting police in the investigation, which has taken authorities to areas across the country, including Florida and Arizona. A local news report claimed Palmer might be in Mexico, but the source said it's believed he's currently hiding out in another state.

Police say Palmer became increasingly enraged over "domestic issues" between Tammy and her estranged husband, Palmer’s son John. Tammy Palmer had reportedly filed an order of protection against her husband, meaning John could not step foot on the 3 1/2 acres of land where both Tammy and Eugene lived in homes close to each another.

Palmer's two sons, John and Clarence, could not be reached for interviews.

The family previously told the Journal News that Palmer acted out of character and snapped that morning, suggesting the alleged murder was not planned in advance. They told the newspaper Palmer fled the scene in his slippers, leaving his breakfast uneaten on his kitchen table.

"If the police didn't botch the hunt in the beginning, my father's remains would be where they belong," Clarence Palmer told the newspaper in 2013. "They were afraid of going into the woods; afraid of a man with a shotgun, supposedly. If he wanted to be found, he would have finished himself off here. He went into the woods. I think he fell into a diabetic coma."

Lutz and his team have always been dubious of such a claim.

"I don't know how you'd know what somebody was wearing unless you were actually looking at them," Lutz said. "He waited for his grandchildren to get on the bus before executing their mother. That's pretty cold-blooded."

Cristina Corbin is a Fox News reporter based in New York. Follow her on Twitter @CristinaCorbin.