Pretty sure there is a connection. My cholesterol was 277 when my TSH was 130. After only 4 weeks on 75 mcg Synthroid, my cholesterol dropped to 177 and TSH down to 4.75. Haven't had cholesterol checked since (June), but I did read there was a connection somewhere in my internet research. Check Mary Shomon's website:
thyroid.about.com
I can't answer for hyperthyroid but there is a connection between hypothyroidism and elevated Cholesterol. As well as elevated Testosterone (such as you might find with P.C.O.S. patients) & elevated Cholesterol.