I was on Carbimzole but my hair fell out before, during (when my dose was adjusted) and after stopping it on the advice of my specialist. So, like Gill, I think it is happening due to being hyper rather than Carbimazole itself. At the moment I have lost most of my hair on the right side and right crown/top of my head and the hair on the left is thinning. Ironically, the hair at the front and the back is fine. Well, there hair is still there and seems to be present and holding but the texture has changed and the hair is finer than it used to be.
I am due to have a thyroidectomy shortly (I was told to stop the drugs to check whether I was euthyroid - I am not) but I am off to buy a couple of wigs as I suspect it is going to take a while to balance my hormones afterwards and, knowing my luck, what's left of my hair will disappear sharpish!
I know I am being flippant but so much has happened with this illness that I have to laugh otherwise I would spend most of my time crying...