  We consider a rough differential equation of the form \(dY_t=\sum_i
V_i(Y_t)d\boldsymbol{X}^i_t+V_0(Y_t)dt \), where \(\boldsymbol{X}_t \) is a
Markovian rough path. We demonstrate that if the vector fields \((V_i)_{0\leq
i\leq d} \) satisfy H\"ormander's bracket generating condition, then \(Y_t\)
admits a smooth density with a Gaussian type upper bound, given that the
generator of \(X_t\) satisfy certain non-degenerate conditions. The main new
ingredient of this paper is the study of non-degenerate property of the
Jacobian process of \(X_t\).
