The actor Gene Hackman was found dead in a mud room in his New Mexico home and his wife, Betsy Arakawa, was found dead on the floor of a bathroom on Wednesday, according to a search warrant affidavit. An open prescription bottle and scattered pills were discovered near her body on a counter in the bathroom.

A dead German shepherd was found between 10 and 15 feet away from Ms. Arakawa in a closet of the bathroom, the affidavit said. There were no obvious signs of a gas leak in the home, it said, and the Fire Department did not find signs of a carbon monoxide leak.

Detective Roy Arndt wrote in the affidavit that sheriff’s deputies reported to the home on Wednesday afternoon after a maintenance worker made an emergency call. One of the deputies found Ms. Arakawa lying on her side on the bathroom floor with a space heater near her head, the affidavit said. The deputy who found her said he suspected that the heater could have fallen with Ms. Arakawa, the filing said.

Ms. Arakawa’s body showed signs of decomposition, the affidavit said. The dead dog was found near her in a closet, and two other dogs were found alive on the property.

The deputies found Ms. Arakawa first and then discovered Mr. Hackman lying in the mud room, with his body in a similar condition to his wife’s, the affidavit said. He was found in gray sweatpants, a blue long-sleeve T-shirt, brown slippers and with a cane, the affidavit said. A pair of sunglasses was found to his left. One of the deputies on the scene said that it appeared he had “suddenly fallen,” the affidavit said.

Sheriff Adan Mendoza of Santa Fe County said in a phone interview that investigators were still trying to determine what caused their deaths, noting that there were no obvious signs of trauma to the bodies and that no note had been found. The sheriff said the home was continuing to be searched on Thursday.

“At this stage in the process there isn’t anything obvious like that,” he said. “The autopsy is going to tell us more.”

Mr. Hackman was nominated for five Academy Awards and won two during his 40-year career. He appeared in films that were seen by millions, including “Bonnie and Clyde,” “The French Connection,” “The Poseidon Adventure,” “Mississippi Burning,” “Unforgiven,” “Superman,” “Hoosiers” and “The Royal Tenenbaums.”

A previous statement sent out early Thursday by the sheriff’s office said that foul play was not suspected. In the affidavit seeking the search warrant, Detective Arndt wrote that he believed that “the circumstances surrounding the death of the two deceased individuals to be suspicious enough in nature to require a thorough search and investigation.”

A magistrate judge granted the search warrant, so that the authorities could collect items from the home, including documents, any narcotics found, and flammable substances, among other things.

The couple was found in their home in a secluded neighborhood high above downtown Santa Fe, with winding roads and views of the mountains.

Mr. Hackman moved to Santa Fe County in the 1980s after filming some movies there. After he quietly retired from Hollywood more than two decades ago, he wrote several historical adventure novels with a friend, Daniel Lenihan. He was seen from time to time in downtown Santa Fe.

Barbara Lenihan, Mr. Lenihan’s wife and a friend of the couple’s who has known them for more than 30 years, said she last spoke with Ms. Arakawa, who is a partner in her local home décor business, in January. Mr. Hackman seemed to be growing frailer, she said, but he was still painting and drawing.

“They always were somewhat reclusive even though everyone loved to be around them,” she said.

Kirsten Noyes contributed reporting.