I wish I had the resources to do this; it would be interesting.
It's been speculated by some "psychics" (if you want to use that term) that schizophrenia is some kind of massive activation of sensitivities to spirits, astral forces etc. While I personally doubt this, it would still be interesting, nonetheless, to carry out an experiment along these lines:
1. Take brain scans of various psychics in mentally concentrated states. An astral projector while he's projecting, a remote viewer while he's viewing, and so forth, and try to identify what happens in the brain that reflects these altered states. Compare, of course, with normal brain scans from other individuals (and with brain scans of the psychics while they are not employing their powers to be sure it's not just some abnormality or peculiarity of their own brain).
2. Take brain scans of schizophrenics and compare them with the "psychic-active" scans of the psychics. Compare and contrast.
3. Have the schizophrenics talk with the psychics about their experiences, and then have the psychics rate them on whether they think the schizophrenics are having legitimate experiences or whether it's just the ramblings of a messed-up brain.
Would be interesting to see the results. I would bet my money that schizophrenia would come up different from the legit psychic experiences, but you never know until you try, right?