  A non-Hermitian operator that is related to its adjoint through a similarity
transformation is defined as a pseudo-Hermitian operator. We study the
level-statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes Quantum
Phase Transition (QPT). We find that the level-spacing distribution of this
Hamiltonian near the integrable limit is close to Poisson distribution, while
it is Wigner distribution for the ranges of the parameters for which the
Hamiltonian is non-integrable. We show that the assertion in the context of the
standard Dicke model that QPT is a precursor to a change in the level
statistics is not valid in general.
