The morphology-dependent resonances (MDRs) in a dielectric sphere that contains many tiny inclusions are studied by use of a recently developed degenerate perturbation method. Degenerate MDRs in the sphere split into multiplets because of the loss of spherical symmetry and manifest themselves as broadened spectral lines in the scattering cross section. Furthermore, the distribution of MDRs in a multiplet is found to obey Wigner's semicircular theorem.