  In this paper we consider the critical group of finite connected graphs which
admit harmonic actions by the dihedral group $D_n$. In particular, we show that
if the orbits of the $D_n$-action all have either $n$ or $2n$ points then 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.
