Animals are being killed and maimed by a "demented psychopath'' on the New South Wales central coast, sparking fears the crimes will escalate.

In the past two weeks three mutilated kangaroos, two beheaded parrots, several savaged rabbits and what is thought to be a decapitated dog or sheep have been found, The Sunday Telegraph reported.

The animals were dumped in water or at the water's edge at separate sites at Point Clare and Avoca Lagoon.

Concerned local police have assigned an officer to collate the incidents and investigate links.

Brisbane Water crime co-ordinator Senior Sergeant Vivienne Crawford said many of the animal carcasses had been disposed of before they could be examined for clues.

Criminologist Dr John Clarke said the history of serial killers was littered with examples of men who began by torturing animals.

"We don't know why, but the homicidal triad is animal cruelty, setting fires and bed-wetting after the age of about nine,'' he said.

"Animal dismemberment teaches the killer how to cut up and dispose of bodies.

"This person may well be a psychopath. If it's an adult, he's probably torturing humans at the same time.

"The police should look at other crime in the area, because animal cruelty also has huge links to sexual homicide and domestic violence. It's about power and control.''

Gosford Mayor Chris Holstein said he was concerned someone in the community was carrying out horrific acts of cruelty.

"Whoever is doing it is an evil, demented psychopath and must be caught and made to bear the full weight of the law,'' he said.

"Anyone who has information on the killer or killers must come forward as a matter of priority.''

Last week, mother-of-three Rikki Phillis, 24, was walking at Avoca Lagoon with her young sons when they discovered the bloated, decapitated remains of a sheep or a dog.

"It's creepy; it's horrible,'' she said.

"If someone can do these terrible things to an animal, what would they do to a human?''

RSPCA chief inspector David O'Shannessy said: "The RSPCA is extremely concerned about the apparent horrific acts of cruelty, which may be being perpetrated on animals.''