It is usually performed under local anesthesia

Yea, if required.

You are asking the question of getting general anesthesia for a thyroid biopsy. I am guessing that you have an identified thyroid nodule and that your doctor is recommending a thyroid biopsy. Generally these nodules are accessible by experienced physicians by needle biopsy and general anesthesia is not necessary. If you are feeling nervous about this procedure I suggest that you ask your physician to prescribe a medication to be taken orally an hour or so riot to the biopsy which can allow you to be less nervous about this test. Good luck.