  We find a series of non-Abelian topological phases that are separated from
the deconfined phase of Z_N gauge theory by a continuous quantum phase
transition. These non-Abelian states, which we refer to as the "twisted" Z_N
states, are described by a recently studied $U(1) \times U(1) \rtimes Z_2$
Chern-Simons (CS) field theory. The $U(1) \times U(1) \rtimes Z_2$ CS theory
provides a way of gauging the global Z_2 electric-magnetic symmetry of the
Abelian Z_N phases, yielding the twisted Z_N states. We introduce a parton
construction to describe the Abelian Z_N phases in terms of integer quantum
Hall states, which then allows us to obtain the non-Abelian states from a
theory of Z_2 fractionalization. The non-Abelian twisted Z_N states do not have
topologically protected gapless edge modes and, for N > 2, break time-reversal
symmetry.
