Schizophrenics are capable of tickling themselves because of their difficulties recognizing their own actions in advance. Tickling yourself is impossible in most people for the same reason that punching others seems half as forceful as it really is — your body offsets your own force. When you tickle yourself, your brain offsets that force and doesn’t respond the tickling.
Schizophrenia, which makes people have trouble understanding their own actions, apparently results in a loss of the neural circuitry for this offsetting. This means that when schizophrenics tickle themselves, it’s as though someone else is doing the tickling. Of course, when other people tickle you, you can actually get tickled.
So yes, schizophrenics, because they dissociate from their own actions on a neurological basis, can tickle themselves.