  We investigate the perturbative aspects of Rozansky-Witten's 3d
$\sigma$-model using Costello's approach to the Batalin-Vilkovisky (BV)
formalism. We show that the BV quantization (in Costello's sense) of the model,
which produces a perturbative quantum field theory, can be obtained via the
configuration space method of regularization due to Kontsevich and
Axelrod-Singer. We also study the factorization algebra structure for quantum
observables following Costello-Gwilliam. In particular, we show that the
cohomology of local quantum observables on a genus $g$ handle body is given by
$H^*(X,(\wedge^*T_X)^{\otimes g})$ (where $X$ is the target manifold), and
prove that the partition function reproduces the Rozansky-Witten invariants.
