I need to repair leaking water supply to bathtub. This tub has supply coming through the body of the tub, so there is no wall access. Do I have to open the ceiling below tub to replace water supply? There is no access door on tub.

Most builders install a tub access panel ,(see image) behind the front of the tub form servicing the tub. Would cutting a access panel help you to get to the leak? Back to you, Tom

"tub has supply coming through the body " can you post a picture of this? Tubs are basically hollow and the supply is easily seen from the back side. Is there a closet or some other room directly behind the tub valve?