  The electric dipole moment of the muon ($d_\mu$) is evaluated in a two Higgs
doublet model with a softly broken discrete symmetry. For $\tan\beta \equiv
|v_2|/|v_1| \sim 1$, contributions from two loop diagrams involving the $t$
quark and the $W$ boson dominate; while for $\tan\beta \gsim 10$, contributions
from two loop diagrams involving the $b$ quark and the $\tau$ lepton are
dominant. For $8 \gsim \tan\beta \gsim 4$, significant cancellation occurs
among the contributions from two loop diagrams and the one loop contribution
dominates for $\tan\beta \sim 7$. For $\tan\beta \gsim 15$, the calculated
$d_\mu$ can be close to the reach of a recently proposed experiment at the
Brookhaven National Laboratory.
