  Recent numerical simulations have shown the strong impact of helicity on
\ADD{homogeneous} rotating hydrodynamic turbulence. The main effect can be
summarized through the following law, $n+\tilde n = -4$, where $n$ and $\tilde
n$ are respectively the power law indices of the one-dimensional energy and
helicity spectra. We investigate this rotating turbulence problem in the small
Rossby number limit by using the asymptotic weak turbulence theory derived
previously. We show that the empirical law is an exact solution of the helicity
equation where the power law indices correspond to perpendicular (to the
rotation axis) wave number spectra. It is proposed that when the cascade
towards small-scales tends to be dominated by the helicity flux the solution
tends to $\tilde n = -2$, whereas it is $\tilde n = -3/2$ when the energy flux
dominates. The latter solution is compatible with the so-called maximal
helicity state previously observed numerically and derived theoretically in the
weak turbulence regime when only the energy equation is used, whereas the
former solution is constrained by a locality condition.
