  The invariant integration method for Chern-Simons theory defined on the
compact hyperbolic manifold {\Gamma}\H^3 is verified in the semiclassical
approximation. The semiclassical limit for the partition function is presented.
We discuss briefly L^2 - analytic torsion and the eta invariant of
Atiyah-Patodi-Singer for compact hyperbolic 3-manifolds.
