Conclusion
  Thyroid hormone is essential for normal bone turnover. Excessive thyroid hormone levels, either of endogenous origin or by thyroid hormone replacement, resulting in TSH-suppression, leads to bone loss. The latter appears partially reversible after adequate treatment, yet an increased risk for osteoporosis may persist. Therefore, it appears prudent to assess bone mineral density in subjects with thyrotoxicosis and subjects on hormone replacement therapy with suppressed TSH. Bisphosphonates and estrogen replacement therapy may prevent the detrimental effects of excessive thyroid hormone on bone.

Hypothyroidism itself seems to have little (clinically significant) effect on the skeleton.