  We first show that the quasiclassical limit of the squared eigenfunction
symmetry constraint of the Sato operator for the mKP hierarchy leads to a
reduction of the Sato function for the dispersionless mKP hierarchy. The
constrained dispersionless mKP hierarchy (cdmKPH) is obtained and it is shown
that the (2+1)-dimensional dispersionless mKP hierarchy is decomposed to two
(1+1)-dimensional hierarchies of hydrodynamical type. The dispersionless mKP
hierarchy with self-consistent sources (dmKPHSCS) together with its associated
conservation equations are also constructed. Some solutions of dmKPESCS are
obtained by hodograph reduction method.
