What are the oxidation states in Borohydride (BH4-)
I would have expected the oxidation states to be +III for B and -I for
  H.


You're right, boron is in the (+3) oxidation state in these equations.

In $\ce{B(OH)_3}$ each $\ce{OH}$ is (-1) and the boron is (+3), overall the molecule is neutral

In $\ce{BH_{4}^{-}}$ each $\ce{H}$ is (-1) and the boron is (+3), overall the ion is (-1)