In Oct 2009 the Jamison family drove up Planola Mountain, then disappeared. Investigators found a twisted trail of evidence, including; a puppy left for dead in the truck, a creepy cellphone picture of the little girl, possible drug links (large amounts of cash, strange behavior caught on security cameras), marital stress (medical conditions, fights, hateful letters), a missing pistol, a white supremacist tenet (the wife being part Native American), talk of evil spirits, and claims of witchcraft. Yup, on top of all the other turmoil, the wife claimed to be a witch, and the husband thought there were four evil spirits living on their roof.
The wife offered to make witch's brew for friends, and vandalized local signs and other objects, after her cat was killed. Including spray-painting, 'witches don't like having their cats killed,' on the side her storage unit. Meanwhile, her husband went shopping for bullets that could kill ghosts. Yeah, you read that right, kill ghosts. Go ahead and take a moment to process that, no one's timing you.
Investigators were baffled, unable to eliminate any of the possibilities, except finding the tenant had a reliable alibi. Their remains were found in Nov 2013, but no cause of death could be determined. It's likely we'll never know exactly what went down that day.
And their tale is not alone, several other newsworthy crimes from recent years have some connection with the paranormal; amateur ghost-hunters accidentally burned down a historic mansion, multiple people have been killed in supposed exorcisms, and mobs have hunted down supposed witches (though, usually in more remote locations).
Historically there's also several criminal cases worth note. One that most Americans are familiar with would be the Amityville case, in which the murder claimed voices (presumed to be demons) made him do it. Similarly, a plethora of murderers (often cannibalistic) throughout history have blamed witches or demons, for turning them into werewolves. In many cases it's likely a tactic to absolve one's self of the sin, saying the devil made me do it, or at least an attempt to seem crazy enough to be treated differently from a regular murderer.
Then there's the law enforcement side of things:
Several police departments are said to have had breakthrough working with psychic investigators, and about a third of US police departments have accepted info from them in some way. Some success in narrowing down the locations of murder victim's bodies using a pendulum and map, has also been reported.
Of course, they're not without their critics, who claim that most force their previous predictions to fit after the case has been solved, and there are also several prominent cases where what the so-called psychic's claimed was so far off the truth it hurt family members of the victims, such as telling them family members were alive/dead when they weren't. Scientific studies have found no evidence that psychics had any advantage over police in identifying crimes when presented with partial evidence. Most police agencies do not officially work with psychics, and even FBI officials have stated they should only be consulted as a last resort. Some psychics on the other hand, claim police organizations claim not to use psychic, so they can hog all the credit for solving the case.
Sometimes the result is in between, such as when Cheryl Carroll-Lagerwey lead police to where she'd seen the body of a missing child in a dream, but what they found there was an adult woman's body.
Resources and Further Reading/Viewing:
“America's Haunted Houses” (TV Special)
“Disappeared”, Paradise Lost (2010, TV Series)
“Ghost Hunters Burn Down Historic Mansion”
Live Science, (posted 2013, 11, 27)
“Jamison family disappearance”
Wikipedia, (last modified 2015, 1, 9)
“MysteryQuest”, Return of the Amityville Horror (TV Series)
Wikipedia, (last modified 2015, 1, 3)
Wikipedia, (last modified 2015, 1, 1)