Basically, people with bipolar disorder appear to have a higher frequency of autoimmune thyroid disease, and family members of bipolar patients appear to have a higher frequency of autoimmune thyroid disease. What isn't really known is the exact nature of the connection. Do thyroid hormone swings mimic bipolar symptoms in some people? Is bipolar caused by a separate autoimmune condition (people with one autoimmune condition are more prone to a second) and the connection is just a predisposition to autoimmune disease?
Certainly thyroid disease is known to cause depression, anxiety, and sometimes (rarely) psychosis. Anyone with bipolar symptoms should probably be checked for thyroid disease (including antibodies) since certainly the co-occurence of untreated thyroid disease would only make bipolar worse.