The force, which covers Mid and West Wales, has received 86 reports of witches in the last five years.
The force's police incident log reveals details of the calls. One caller reported "that one individual is a witch and had attended at the house to put salt around the bed".
A caller in January last year claimed he had been fed a "fur ball" during a witchcraft ritual.
Following a call from Llanelli, police recorded: "Caller, who was drunk, who rang regarding a gang of witches who want to sacrifice him."
Another call was a report of a "malicious communication: rumours that an individual's mother is a witch".
The details released to Wales on Sunday under the Freedom of Information Act have revealed the counties of Powys, Ceredigion, Carmarthenshire and Pembrokeshire are awash with reports of weird goings-on.
In addition to calls about witches in the past five years, the force has received one call about a werewolf, seven about vampires, 19 about UFOs, 13 about big cats, 73 reports of ghosts, 16 of zombies, 35 of demons, five regarding big foot sightings, 33 of monsters and 18 about wizards.
Haverfordwest appears to be the real hotbed of ghostly activity.
On the same day, one caller reported "that they had seen their father as a ghost", while another call to the police was "regarding concern for safety - reporting that an individual is stating that 'ghosts' are going to kill them".
In Lampeter, police dealt with a call "reporting concern for safety, individual believes they are a vampire".
Paranormal investigator and writer, the Rev Lionel Fanthorpe, from Cardiff, said there could be a number of explanations for the reports.
He said: "Powys comes up pretty frequently in terms of sightings of unusual things.
"I share the investigative attitude of Charles Hoy Fort, who said nothing was too ridiculous to investigate because it might be real.
"We can most closely associate werewolves with tales of spectral hounds like that of Shuck in North Norfolk.
"But the power of the human mind is unlimited. There was a Victorian explorer called Alexandra David-Neel, who went to Tibet to study a teaching tool, called a Tupla, which says the mind creates the world of appearances, it can create any particular object desired.
"It's like imagining something so powerfully that witnesses can see your dream. Another idea is that it is a recording in the fabric of a building or landscape. Or it can just be an active imagination. The human mind abhors a vacuum."
Richard Holland, an author on the paranormal from Clwyd, who runs websites www.uncannyuk.com and www.paranormalmagazine.co.uk, said he was not surprised to find so many reports of witches, ghosts and other fantastical characters.
"Wales is a frighteningly haunted country," he said. "Every day, it seems, someone in Wales sees an apparition or experiences NOTE: I have a psychic friend in Wales who, by the way, has remarkable a ability and tells me a helluva lot of what's going on there. Since 2007, there have been 67 posts on 'Phantoms and Monsters'
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