My problem is a bit different
-Water leaks down to 1st floor when showering and drain is Open -
-Does not leak with drain Closed when showering - opening drain afterwards to drain tub does not cause a leak
-A bath with drain closed and then opened does not produce a leak
Any Ideas?

Speedball1 will probably be here in a few moments and maybe he can figure this one out. The only thing that comes to mind would involve the tub flexing due to your body weight, is it fiberglass or plastic?

This is a real head scratcher. I hope you have a access panel behind the front of the tub because you're going to hafta get back there to see where the water's coming from. If there is no access panel then make one in the wall behind the drain. The only other option is opening up the ceiling. You MUST locate the source before you can began the repair. Good luck and let me know what you find. Tom