Could rhodiola cause low tsh levels?

Very unlikely: There is no known effect of rhodiola on the hypothalamus, pituitary or thyroid gland. Low TSH is almost always associated with hyperthyroidism or a pituitary problem. See an endocrinologist for evaluation.

Unlikely but...: Rhodiola is known to improve thyroid function and thus might be expected to reduce TSH levels somewhat (though more research on this is needed). However, a low TSH tends to be a sign of hyperthyroidism and, as far as i know, rhodiola is not known to stimulate the thyroid to the point of hyperthyroidism.