Is there any connection between the vitiligo and thyroid disorders?

Both are autoimmune: Both hypothyroidism and vitiligo are autoimmune conditions, caused by antibodies. In the case of hypothyroidism they cause inflammation in the thyroid and subsequent hypo activity; in vitiligo they cause lack of skin pigmentation.

Can be: Many thyroid problems are due to automimunity, and vitiligo is also caused by autoimmunity. Autoimmunity means that one's immune system is making abnormal antibodies that target one's own proteins. So it is not true that thyroid problems cause vitiligo, or vitiligo causes thyroid problems, it is true that autoimmunity (hereditary) causes both.

Strong Association: There is a significant association between thyroid disease and vitiligo. Many patients with vitiligo have increased antithyroid autoantibodies. Furthermore mutations in the gene nalp1, a regulator of innate immunity, has been shown to be present in patients with autoimmune diseases including thyroid disease and vitiligo.