  We study three-dimensional gauge theories based on orthogonal groups.
Depending on the global form of the group these theories admit discrete
$\theta$-parameters, which control the weights in the sum over topologically
distinct gauge bundles. We derive level-rank duality for these topological
field theories. Our results may also be viewed as level-rank duality for
$SO(N)_{K}$ Chern-Simons theory in the presence of background fields for
discrete global symmetries. In particular, we include the required counterterms
and analysis of the anomalies. We couple our theories to charged matter and
determine how these counterterms are shifted by integrating out massive
fermions. By gauging discrete global symmetries we derive new boson-fermion
dualities for vector matter, and present the phase diagram of theories with
two-index tensor fermions, thus extending previous results for $SO(N)$ to other
global forms of the gauge group.
