Pat the Peacock arrived in Thimbleby, near Northallerton in North Yorkshire two years ago, but has not been seen since 6 September.
Online complaints from visitors to a cottage in the village said the bird's noise "spoiled the holiday".
One villager told the BBC's Jeremy Vine show: "I know who killed the blooming thing and I'm glad he's gone."
North Yorkshire Police said there had been no evidence of foul play.
A village resident claims to have confronted a man and a woman below the tree where the tame peacock roosted each night, on 6 September, after seeing torchlight and hearing gunshots.
The pair said they were "shooting rabbits", and the resident saw no evidence of the body of the bird.
A tourist who had stayed at a holiday cottage in the village said in an online review: "In all conscience I cannot recommend this cottage if you value your sleep."
The review continues: "It really did spoil our holiday as we were woken up every night [from around 03:00] and he just continued to call and squawk."
A caller to the BBC Radio 2 Jeremy Vine show, who would not give his real name, said a "very good friend" of his had killed Pat the Peacock.
"A lot of people in our village were absolutely sick to the back teeth of the blooming thing," the caller said.
"I know who killed the blooming thing and I'm glad he's gone.
"We're only a little village and we need people coming [to stay] here and use the local pub.
"I'm sorry the little thing is dead but at the end of the day, he was a nuisance."
A peacock that vanished from a village after online complaints about it being too noisy is thought to have been shot.