Yes it does, but it can also go clockwise.
The misconception here is a misunderstanding of the
coriolis effect which affects which way cyclones spin and oceanic and atmospheric currents spin. It is not strong enough to work on a couple hundred liters of water in your bath. You can get water to spin both ways down the plug hole in both hemispheres.
The main things that govern which way the water spins are the shape of the bowl and any pertubations that are left over from filling the bowl or using the water.