  We study the conditions of maximal $CP$ violation in the neutral Higgs mass
matrix of the two Higgs doublet model. We get fixed values of $\tan\b$ and
constraints on the Higgs potential parameters. Two neutral Higgs scalars are
constrained to be lighter than the charged Higgs scalar and these two Higgs
scalars are expected to be almost degenerate due to the smallness of the $h$
parameter, where $h$ is the CP violating coupling constant of the Higgs
interaction. The radiative correction of the $\rho$ parameter from the Higgs
scalar exchange is rather small and its sign negative for a wide range of Higgs
masses. It follows that maximum $CP$ violation in the two Higgs doublet model
is safely allowed for the $\rho$ parameter without the custodial symmetry.
