Wet Adjacent wall and base board behind bath tub
The leak is probably either in the supply lines and valve, or in the drain pipes. It's also possible that a vent through the roof is leaking rainwater. The only way to determine the cause with confidence is to have a look. 

Are you sure that there's no access to the tub's plumbing from the back side or below? If not, consider installing an access panel at an appropriate location in your wall or ceiling.



This is a DIY site, so if you're not up to that task as a starting point, you probably need a professional.