  The Grobe-Haake-Sommers (GHS) conjecture generalizes the
Bohigas-Giannoni-Schmit conjecture to dissipative systems, connecting
classically chaotic systems with quantum spectra that exhibit level repulsion
as predicted by Ginibre ensembles. Here, we show that the GHS conjecture does
not hold for the open Dicke model, which is a spin-boson model of experimental
interest. Surprisingly, where the open quantum model shows Ginibre level
statistics, we do not always find evidence of chaotic structures in the
classical limit. This result challenges the universality of the GHS conjecture
and raises the question of what is the source of spectral correlations in open
quantum systems.
