  We discuss Higgs boson decays in the CP-violating MSSM, and examine their
phenomenological impact using cross section limits from the LEP Higgs searches.
This includes a discussion of the full 1-loop results for the partial decay
widths of neutral Higgs bosons into lighter neutral Higgs bosons (h_a -> h_b
h_c) and of neutral Higgs bosons into fermions (h_a -> f fbar). In calculating
the genuine vertex corrections, we take into account the full spectrum of
supersymmetric particles and all complex phases of the supersymmetric
parameters. These genuine vertex corrections are supplemented with Higgs
propagator corrections incorporating the full one-loop and the dominant
two-loop contributions, and we illustrate a method of consistently treating
diagrams involving mixing with Goldstone and Z bosons. In particular, the
genuine vertex corrections to the process h_a -> h_b h_c are found to be very
large and, where this process is kinematically allowed, can have a significant
effect on the regions of the CPX benchmark scenario which can be excluded by
the results of the Higgs searches at LEP. However, there remains an unexcluded
region of CPX parameter space at a lightest neutral Higgs boson mass of ~45
GeV. In the analysis, we pay particular attention to the conversion between
parameters defined in different renormalisation schemes and are therefore able
to make a comparison to the results found using renormalisation group
improved/effective potential calculations.
