Put the stopper in the tub and fill with a small amount of water. Lay a few pieces of paper on the floor under the pipes where you suspect the water is dripping, Have your helper remove the stopper while you shine a flashlight on the drain. You should be able to confirm that it is the drain that is leaking.
The drain plug of your hot tub is designed for just this purpose. It's not hard to use the drain plug, and employing the plug to empty out the water is the first.
Hot tub leaks may seem hard to find, but it's not difficult if you know where to start.. people (so that they do not have to drain the spa water to replace a pump).