Police said the animal was behaving abnormally and so they feared it was sick and dangerous when they shot it, KNXV-TV, Phoenix, reported.
Arizona Game and Fish Department officers were on the scene when the big cat was killed as it tried to escape into the mountains. State officials took the animal away for rabies testing, KTVK-TV, Phoenix, reported.
The mountain lion first appeared at the back door of the home of Rebekah Coleman, who said she was watching TV with her family when all of a sudden they saw a pair of green eyes staring at them, KTVK-TV said.
"He showed no fear at all," said Coleman who shot video of the lion looking in her back door, KNXV-TV reported. "He had with big ears, saucer-sized paws and empty green eyes."
She said the cat was very skinny and looked hungry.
"I think he was ready to do whatever it took to find a meal," she said.
The lion stared through Coleman's door for a few minutes then leaped an 8-foot fence into Rebekah's neighbors' yard, KNXV reported.
At that point, Coleman called 911, fearing for the neighbor's children and puppies. No one was harmed, KTVK-TV reported.
Several residents said they thought killing the animal was unnecessary. They said they're accustomed to visits from wildlife.