  We consider the behaviour of the distribution for stationary solutions of the
complex Ginzburg-Landau equation perturbed by a random force. It was proved
earlier that if the random force is proportional to the square root of the
viscosity, then the family of stationary measures possesses an accumulation
point as the viscosity goes to zero. We show that if $\mu$ is such point, then
the distributions of the L^2 norm and of the energy possess a density with
respect to the Lebesgue measure. The proofs are based on It\^o's formula and
some properties of local time for semimartingales.
