Depression is a prominent characteristic of women who have polycystic ovary syndrome. Part of the depression stems from the emotional difficulty of being infertile, overweight, too hairy, or having acne, hair loss or some other disturbing symptom.
However, the primary cause of depression in PCOS appears to be hormonal in nature. A number of studies have shown a connection between a negative mood and elevated androgens, which are male hormones such as testosterone. In one interesting study, there was a correlation between the most intense depression and testosterone levels slightly above normal, but not when testosterone was low or extremely high.
Of course, depression is not limited to elevated testosterone.
Depression has also been associated with insulin resistance and depressed thyroid function. Disturbed LH (luteinizing hormone) levels and rhythms have been found in depressed women compared to women who are not depressed. Disturbed LH is a primary reason why you don't ovulate. Abnormal estrogen and cortisol are additional hormonal factors connected to depression.
Women with mixed anxiety-depression disorder have high levels of homocysteine in the follicular and luteal phase of the menstrual cycle, and they have higher blood homocysteine levels as compared to healthy women. Women with PCOS commonly have elevated homocysteine, which is a byproduct of metabolic activity. Normally, homocysteine is broken down and made harmless.
However, a poor diet that is deficient in calcium and B vitamins, and drugs such as Metformin (Glucophage) help to elevate homocysteine.
All of the above factors for depression are common in PCOS women. There are additional factors that we won't go into here. But you can see that if you have PCOS and depression, you have a complex situation on your hands, a situation that does not have a simple solution.
The good news is that you can favorably alter your hormones and thus lift your depression at least to some extent with a healthy diet, regular exercise, stress management, selected nutritional supplements, and possibly medications.
The diet would include plenty of whole, fresh vegetables, fresh fruit in moderation, fish, poultry, some other meats, nuts and seeds in moderation, greatly reduced consumption of grain products, and possible reduction of some legumes. As for nutritional supplements, a high quality multi-vitamin/mineral would be a good place to start.
Sources
Dr. Nancy Dunne,
Androgens and mood dysfunction in women: comparison of women with polycystic ovarian syndrome to healthy controls, Psychosom Med. 2004 May-Jun;66(3):356-62
Depression and PCOS 
