Updated December 04, 2014.
Patients with a low TSH who are taking statin drugs -- drugs to lower cholesterol -- are three to four times likely to have normal radioiodine uptakes and scans that patients not taking a statin drug. Researchers speculate that either statins are improving or modifying the hyperthyroidism (possibly due to the antiinflammatory effect), or they may be causing falsely low TSH levels. (This situation, where the thyroid is normal but TSH levels are low, is called pseudohyperthyroidism.)
Seth D. Yandell, William C. Harvey, Neil J. Fernandes, Patrick W. Barr, Mark Feldman. Thyroid. October 1, 2008, 18(10): 1039-1042
Interestingly, there is also evidence that the statin drug simvastatin (Zocor) can improve Hashimoto's Thyroiditis.
Patients with Hashimoto's Thyroiditis were given 20 mg/day of simvastatin for 8 weeks. After 8 weeks, the patients taking simvastatin had increased Free T3 and Free T4 and decreased TSH levels, as well as emphasis of improved immune system modulation and activity.
Gullu S, et. al. "In vivo and in vitro effects of statins on lymphocytes in patients with Hashimoto's thyroiditis." Eur J Endocrinol. 2005 Jul;153(1):41-8