Sanders KM, Stuart AL, Williamson EJ, et al. Annual high-dose vitamin D3 and mental well-being: randomised controlled trial. Br J Psychiatry. May 2011;198(5):357-364.
Yes, low levels of vitamin D are associated with depression, schizophrenia and seasonal affective disorder. Please see the following RG links and PDF attachment.
Article Prevalence and Correlates of Vitamin D Deficiency in a Sampl...
Article Vitamin D deficiency and psychological disorders
Article Vitamin D and Depression: Cellular and Regulatory Mechanisms
Article Vitamin D in schizophrenia: A clinical review
Article Vitamin D in Anxiety and Affective Disorders