  We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over
2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation,
previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to
this case. This reduces the non-Abelian theory on $M$ to a 2-dimensional
Abelian theory on $\Sigma$ which we identify with q-deformed Yang-Mills theory,
as anticipated by Vafa et al. We compare and contrast our results with those
obtained by Beasley and Witten using the method of non-Abelian localisation,
and determine the surgery and framing presecription implicit in this path
integral evaluation. We also comment on the extension of these methods to BF
theory and other generalisations.
