Gene Hackman and his wife, Betsy Arakawa, tragically died this week ... and their family believes carbon monoxide poisoning is to blame, TMZ has learned.

The legendary actor's daughter, Elizabeth Jean Hackman, tells TMZ they’re not sure, but they think the cause might be from toxic fumes. She added law enforcement found no signs of foul play, although Santa Fe County Sheriff Adan Mendoza tells us they haven't ruled anything out and are still investigating.

The house is fairly modern ... it was built in 2000. We do not know if there were any issues with gas leaks or if there were calls to service at the address.

Mendoza tells us when deputies performed a welfare check at the property Wednesday and found the couple's bodies, gas company and fire department personnel also responded to make sure there were no toxic fumes that would endanger deputies during their search.

Gene and Betsy were found dead at home on Wednesday, along with one of their dogs, also dead, after a neighbor raised concerns.

Elizabeth gives us more insight into Gene’s life before his passing ... saying he and his wife had been living in their New Mexico home since he retired in 2004.

When Gene walked away from Hollywood, he was done for good … spending his retirement painting. She also told us his favorite film was "The French Connection."

Elizabeth didn’t comment on his health -- but he had just turned 95, and in a rare public sighting on March 28, 2024, he was seen walking with a cane and holding his wife’s hand for support.

The family is getting affairs in order now, so there is no word on a service.