  In this paper we consider the critical group of finite connected graphs which
admit harmonic actions by the dihedral group $D_n$, extending earlier work by
the author and Criel Merino. In particular, we show that the critical group of
such a graph can be decomposed in terms of the critical groups of the quotients
of the graph by certain subgroups of the automorphism group. This is analogous
to a theorem of Kani and Rosen which decomposes the Jacobians of algebraic
curves with a $D_n$-action.
