The FAA reference, already quoted above, explains how catagory is determined. It does not say that it does not apply for circling. It does say you can choose to use a higher catagory if you want to take advantage of the higher circling speeds. So even if you can comply with the approach speeds for the catagory you can't drop down a Cat. ie even if you may be flying an aircraft with a Vat of 145 kts and could conceivably fly an approach, including circling, within Cat C speeds that would not be legal. Likewise if your aircraft only just fits into a Cat at max landing weight you can't drop down when at a lower weight.
The is only one type of catagory, that is instrument approach catagory. There is separate circling catagory. Not sure of the legality of operating in one cat for straight-in and another for circling.