The dog found dead alongside Gene Hackman and his wife likely died from a lack of food and water ... according to an animal control agency in New Mexico.

Gene and Betsy Arakawa's kelpie mix, Zinna, likely died from dehydration and starvation ... according to a necropsy obtained by The Associated Press.

The report says the Santa Fe County animal control agency noted the dog's stomach was empty aside from small amounts of bile and hair.

The necropsy also reportedly ruled out infectious disease, trauma and poisoning as potential causes for the dog's death.

It's not a huge surprise the dog wasn't eating or drinking ... the poor pooch was found dead inside a crate in a bathroom closet inside the home where Gene and Betsy's dead bodies were also found.

As we reported ... Gene's official cause of death is heart disease and advanced Alzheimer's ... and Betsy died after contracting Hantavirus, a rare virus spread by rats and mice.

The official timeline says Betsy likely died Feb. 11 and Gene died Feb 18. ... and officials think he didn't know she was dead in the home due to his Alzheimer's.