  We analyze the statistics of resonance widths in a many-body Fermi system
with open decay channels. Depending on the strength of continuum coupling, such
a system reveals growing deviations from the standard chi-square
(Porter-Thomas) width distribution. The deviations emerge from the process of
increasing interaction of intrinsic states through common decay channels; in
the limit of perfect coupling this process leads to the super-radiance phase
transition. The width distribution depends also on the intrinsic dynamics
(chaotic vs regular). The results presented here are important for
understanding the recent experimental data concerning the width distribution
for neutron resonances in nuclei.
