A light vector boson, Z_d, associated with a dark sector U(1)_d gauge group has been introduced to explain certain astrophysical observations as well as low energy laboratory anomalies. In such models, the Higgs boson may decay into X+Z_d, where X=Z, Z_d or gamma. Here, we provide estimates of those decay rates as functions of the Z_d coupling through either mass-mixing (e.g. via an enlarged Higgs mechanism) or through heavy new fermion loops and examine the implied LHC phenomenology. Our studies focus on the higher m_{Z_d} case, > several GeV, where the rates are potentially measurable at the LHC, for interesting regions of parameter spaces, at a level complementary to low energy experimental searches for the Z_d. We also show how measurement of the Z_d polarization (longitudinal versus transverse) can be used to distinguish the physics underlying these rare decays.