At a press conference in Santa Fe on Friday afternoon local time, Police Chief Adan Mendoza says they continue to regard the deaths as "suspicious" even though the investigators do not suspect a crime.
It also emerges that Gene Hackman may have been dead for as long as two weeks. According to Mendoza, Hackman's pacemaker shows the last "entry" on February 17 - which indicates that it was then that he died.
It was a maintenance worker who discovered the bodies of the two-time Oscar winner Gene Hackman, 95, and Betsy Arakawa, 64, on Wednesday at the couple's home in New Mexico.
Hackman was found at the entrance to the house and Arakawa in a bathroom. One of the couple's dogs was also found dead in the home, while two dogs were alive.
The investigators are now trying to determine when someone last saw or spoke to the couple, says Mendoza to NBC's "Today".
It's a challenge since they were two very private people, said the police chief, who also pointed out that the autopsy and the results of toxicological tests may take several months.
The responsible gas company is said to have inspected the gas pipes inside and near Hackman's and Arakawa's home. According to the preliminary reports, no fault was detected in the gas pipes. The fire department has not seen any signs of a gas leak or carbon monoxide poisoning as the cause of the deaths.