  It is shown that the quasi-localized states in weakly disordered systems can
lead to the non-analytical distribution of level curvatures. In 2D systems the
distribution function P(K) has a branching point at K=0. In quasi-1D systems
the non-analyticity at K=0 is very weak, and in 3D metals it is absent at all.
Such a behavior confirms the conjecture that the branching at K=0 is due to the
multi-fractality of wave functions and thus is a generic feature of all
critical eigenstates. The relationsip between the branching power and the
multi-fractality exponent $\eta(2)$ is derived.
