Does Low TSH Level Cause Osteoporosis?

hi id like to ask about Amour medication.. I was always borderling tsh the sometines and quite often with in the healthy range but my t3 and t4 were low.. So i was started on armour of my own choice and research.. the thing that worrie sme and i find doctors dont understand is the low tsh below the normal limit.. is tgis normal for the tsh to be low while the t3 and t4 are in a healthy ranmge now.. Does is cause osteoporosis?