  A Monte Carlo event generator is constructed for a two-Higgs-doublet model
with maximal CP symmetry, the MCPM. The model contains five physical Higgs
bosons; the $\rho'$, behaving similarly to the standard-model Higgs boson, two
extra neutral bosons $h'$ and $h"$, and a charged pair $H^\pm$. The special
feature of the MCPM is that, concerning the Yukawa couplings, the bosons $h'$,
$h"$ and $H^\pm$ couple directly only to the second generation fermions but
with strengths given by the third-generation-fermion masses. Our event
generator allows the simulation of the Drell-Yan-type production processes of
$h'$, $h"$ and $H^\pm$ in proton-proton collisions at LHC energies. Also the
subsequent leptonic decays of these bosons into the $\mu^+ \mu^-$, $\mu^+
\nu_\mu$ and $\mu^- \bar \nu_\mu$ channels are studied as well as the dominant
background processes. We estimate the integrated luminosities needed in $p p$
collisions at center-of-mass energies of 8 TeV and 14 TeV for significant
observations of the Higgs bosons $h'$, $h"$ and $H^\pm$ in these muonic
channels.
