  We study the ensemble of complex symmetric matrices. The ensemble is useful
in the study of effect of dissipation on systems with time reversal invariance.
We consider the nearest neighbor spacing distribution and spacing ratio to
investigate the fluctuation statistics and show that these statistics are
similar to that of dissipative chaotic systems with time reversal invariance.
We show that, unlike cubic repulsion in eigenvalues of Ginibre matrices, these
ensemble exhibits a weaker repulsion. The nearest neighbor spacing distribution
exhibits $P(s) \propto -s^3 \log s$ for small spacings. We verify our results
for quantum kicked rotor with time reversal invariance. We show that the rotor
exhibits similar spacing distribution in dissipative regime. We also discuss a
random matrix model for transition from time reversal invariant to broken case.
