  The muon anomalous magnetic moment exhibits a 3.6 \sigma discrepancy between
experiment and theory. One explanation requires the existence of a light vector
boson, Z_d (the dark Z), with mass 10 - 500 MeV that couples weakly to the
electromagnetic current through kinetic mixing. Support for such a solution
also comes from astrophysics conjectures regarding the utility of a U(1)_d
gauge symmetry in the dark matter sector. In that scenario, we show that mass
mixing between the Z_d and ordinary Z boson introduces a new source of "dark"
parity violation which is potentially observable in atomic and polarized
electron scattering experiments. Restrictive bounds on the mixing (m_{Z_d} /
m_Z) \delta are found from existing atomic parity violation results, \delta^2 <
2 x 10^{-5}. Combined with future planned and proposed polarized electron
scattering experiments, a sensitivity of \delta^2 ~ 10^{-6} is expected to be
reached, thereby complementing direct searches for the Z_d boson.
