The Juelkes and others say the birds roost at the ranch. The couple say their Labrador retriever, Reginald Winthorp, has twice had intestinal illnesses that they blame on bird droppings.
Newton's lawyer, Jay Brown, said the birds aren't Newton's.
"We've never bought a peacock. We've never brought in a peacock," Brown said.
Sure, peacocks and hens were among the exotic menagerie the iconic "Mr. Las Vegas" headliner kept when he lived at the ranch southeast of the Las Vegas Strip. Among them were Arabian horses, penguins, a Capuchin monkey named Boo, and wallabies.
Brown said peafowl were already at the ranch when Newton bought the property in the '60s.
Casa de Shenandoah is officially home to about 25 peafowl that are tagged and live in an enclosure, Brown said.
Newton no longer lives at the estate, which today is a tourist museum focused on Newton's life and career.
Brown said the Newtons are willing to help remove the wild birds, but it wasn't their responsibility.
"These are feral peacocks," he said. "It's a neighborhood problem, not a Newton problem, in fairness."
Neighbor Bart Donovan, a member of a local advisory board, sees it differently.
"These things were born on the Newton property, they live there, they roost there at night," he said. "As far as I'm concerned, they're their birds."
Donovan said he fears the birds wandering in roadways could cause serious accidents.
The exact number of wild peafowl roaming the area around the ranch is unknown. Clark County code enforcement officials guess there are between 20 and 30, the Review-Journal reported.
Compounding the problem is that peafowl have an average life span of 20 years, according to the Los Angeles County Arboretum and Botanic Garden, and peahens can lay three to eight eggs at a time.
"My view is, if we don't stay on top of this, it will become more of a problem because the animals do breed," said Clark County Commissioner Mary Beth Scow, who represents the district. "I know when I was out there, I saw several young peafowl."
County commissioners spent more than 30 minutes at a recent meeting discussing how to best handle the problem.
Animal control has a cage large enough to capture peafowl, but commissioners decided its staff is too small to constantly monitor the trap.
And once the peafowl are caught, there remains the question of what to do with them.
Nevada Department of Wildlife spokesman Doug Nielsen said his agency can't help. He compared the situation to someone raising a pet duckling and releasing it at a local park after it matures.
"At this point, the community is going to have to figure it out and decide what they want to do," Nielsen said.