We discuss a relation between a dynamical zeta function defined by the geodesic flow on a 2-dimensional hyperbolic orbifold and the asymptotic behavior of the Reidemeister torsion for the unit tangent of the orbifold. Here the asymptotic behavior of the Reidemeister torsion means the behavior of the leading term in the Reidemeister torsion defined by the SL(n, C)-representation induced by an SL(2, C)-representation of the fundamental group of a manifold. For a hyperbolic 3-manifold, we can derive the hyperbolic volume from the limit of the leading term in the Reidemeister torsion by observing the asymptotic behavior with a dynamical zeta function according to previous works. For the unit tangent bundle over a 2-dimensional hyperbolic orbifold, which is not a hyperbolic 3-manifold, we will see that the orbifold Euler characteristic of the orbifold appears in the limit of the leading term in the eidemeister torsion for the unit tangent bundle by observing the asymptotic behavior with the dynamical zeta unction defined by the geodesic flow on the orbifold.