I found a recent PLoS article that said that none of hypochondriasis, depression, hysteria, psychopathic deviate, masculinity-femininity, psychasthenia, schizophrenia, or social intraversion (on the MMPI-2) "were associated with any melatonin parameter."
However, it does appear that "increases scores of Hypomania and Paranoia were associated with a shorter DLMO-DLMOff interval" (duration of melatonin production).
The only thing that concerns me are the significance and the effect size of the latter two results. I can't tell whether they corrected for multiple comparisons or not.
Reference: Burgess HJ, Fogg LF (2008) Individual Differences in the Amount and Timing of Salivary Melatonin Secretion. PLoS ONE 3(8): e3055. doi:10.1371/journal.pone.0003055