Gluing formula for an invariant related to the Chern-Simons perturbation theory

The Chern-Simons perturbation theory gives an invariant $d(M,\rho )$ for a pair of a closed oriented 3-manifold $M$ and a representation $\rho$ of the fundamental group. We generalize $d(M,\rho )$ for compact oriented 3-manifolds with torus boundaries. Further we give a gluing formula for $d(M,\rho )$.