  We prove that the Halperin-Carlsson conjecture holds for any free (Z_2)^m
action on a compact manifold whose orbit space is a small cover. In addition,
we show that if the total space of a principal (Z_2)^m bundle over a small
cover is connected, it must be equivalent to a partial quotient of the
corresponding real moment-angle manifold with some canonical Z_2-torus action.
