  We study distributions of eigenvalue curvatures for a block diagonal random
matrix perturbed by a full random matrix. The most natural physical realization
of this model is a quantum chaotic system with some inherent symmetry, such
that its energy levels form two independent subsequences, subject to a generic
perturbation which does not respect the symmetry. We describe analytically a
crossover in the form of a curvature distribution with a tunable parameter
namely the ratio of inter/intra subsystem coupling strengths. We find that the
peak value of the curvature distribution is much more sensitive to the changes
in this parameter than the power law tail behaviour. This observation may help
to clarify some qualitative features of the curvature distributions observed
experimentally in acoustic resonances of quartz blocks.
