  We employ the random matrix theory (RMT) framework to revisit the
distribution of resonance widths in quantum chaotic systems weakly coupled to
the continuum via a finite number M of open channels. In contrast to the
standard first-order perturbation theory treatment we do not a priory assume
the resonance widths being small compared to the mean level spacing. We show
that to the leading order in weak coupling the perturbative $\chi^2_M$
distribution of the resonance widths (in particular, the Porter-Thomas
distribution at M=1) should be corrected by a factor related to a certain
average of the ratio of square roots of the characteristic polynomial
("spectral determinant") of the underlying RMT Hamiltonian. A simple
single-channel expression is obtained that properly approximates the width
distribution also at large resonance overlap, where the Porter-Thomas result is
no longer applicable.
