  We derive general properties of the linear response functions of
nonequilibrium steady states in Langevin systems. These correspond to extension
of the results which were recently found in Hamiltonian systems [A. Shimizu and
T. Yuge, J. Phys. Soc. Jpn. {\bf 79}, 013002 (2010)]. We discuss one of the
properties, the sum rule for the response function, in particular detail. We
show that the sum rule for the response function of the velocity holds in the
underdamped case, whereas it is violated in the overdamped case. This implies
that the overdamped Langevin models should be used with great care. We also
investigate the relation of the sum rule to an equality on the energy
dissipation in nonequilibrium Langevin systems, which was derived by Harada and
Sasa.
