Hackman, 95, was found dead on Wednesday in an entryway, and his 65-year-old wife, Betsy Arakawa, was found in a bathroom next to a space heater, Santa Fe County Sheriff's Office detectives wrote in a search warrant affidavit.
There was an open prescription bottle and pills scattered on a countertop near Arakawa.
Denise Avila, a sheriff's office spokesperson, said there was no indication they had been shot or had any wounds.
The New Mexico Gas Co tested the gas lines in and around the home after the bodies were discovered, according to the warrant.
At the time, it didn't find any signs of problems and the Fire Department found no signs of a carbon monoxide leak or poisoning.
The gruff but beloved Hackman was among the most accomplished actors of his generation, appearing as villains, heroes and antiheroes in dozens of dramas, comedies and action films from the 1960s until his retirement in the early 2000s.
"He was loved and admired by millions around the world for his brilliant acting career, but to us he was always just Dad and Grandpa," his daughters and granddaughter said in a statement on Thursday. "We will miss him sorely and are devastated by the loss."
According to the search warrant affidavit, a maintenance worker reported that the home's front door was open when he arrived to do routine work Wednesday, and he called police after finding the bodies.Â
But in an emergency call, the maintenance worker said he was unable to get inside when the operator asked whether the people in the house were breathing.
"I have no idea," the subdivision's caretaker said. "I am not inside the house. It's closed. It's locked. I can't go in. But I can see she's laying down on the floor from the window."
He and another worker later told authorities that they rarely saw the homeowners and their last contact with them had been about two weeks ago.
Hackman appeared to have fallen, a deputy observed. A cane was nearby.
A dead German shepherd was found in a bathroom closet near Arakawa, police said. Santa Fe County Sheriff Adan Mendoza said during a press conference on Thursday that the dog was found in a kennel. Two healthy dogs were found on the property - one inside and one outside.
"There was no indication of a struggle," Mendoza said.
"There was no indication of anything that was missing from the home or disturbed, you know, that would be indication that there was a crime that had occurred."
Results of autopsies conducted on both bodies were not available yet, sheriff's officials said, noting that carbon monoxide and toxicology test results were pending.
Hackman routinely showed up on Hollywood lists of greatest American actors of the 20th century. He could play virtually any kind of role, from comic book villain Lex Luthor in Superman to a coach finding redemption in the sentimental favourite Hoosiers.
Hackman was a five-time Oscar nominee who won best actor in a leading role for The French Connection in 1972 and best actor in a supporting role for Unforgiven two decades later. His death comes just four days before this year's ceremony.
Tributes quickly poured in from Hollywood.
"There was no finer actor than Gene," actor-director Clint Eastwood, Hackman's "Unforgiven" co-star, said in a statement. "Intense and instinctive. Never a false note. He was also a dear friend whom I will miss very much."
Hackman met Arakawa, a classically trained pianist who grew up in Hawaii, when she was working part-time at a California gym in the mid-1980s. They soon moved in together and relocated to Santa Fe by the end of the decade.
Their Southwestern-style ranch on Old Sunset Trail sits on a hill in a gated community with views of the Rocky Mountains. The sprawling four-bedroom home on 2.4 hectares was built in 1997.
Hackman also co-wrote three novels, starting with the swashbuckler, Wake of the Perdido Star, with Daniel Lenihan in 1999, according to publisher Simon & Schuster. He then penned two by himself, concluding with Pursuit in 2013, about a female police officer on the tail of a predator.
In his first couple of decades in New Mexico, Hackman was often seen around the historic state capital, known as an artist enclave, tourism destination and retreat for celebrities.
In recent years, he was far less visible, though even the most mundane outings caught the attention of the press.
Aside from appearances at awards shows, he was rarely seen in the Hollywood social circuit and retired from acting about 20 years ago. His was the rare Hollywood retirement that actually lasted.
Hackman had three children from a previous marriage. He and Arakawa had no children together but were known for having German shepherds.
