  We study three dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-Matter
theories on the direct product of a circle and a two dimensional hemisphere
($S^1 \times D^2$) with specified boundary conditions by the method of
localization. We construct boundary interactions to cancel the supersymmetric
variation of the three dimensional superpotential term and the Chern-Simons
term and show inflows of the bulk-boundary anomalies. It finds that the
boundary conditions induce two dimensional $\mathcal{N}=(0,2)$ type
supersymmetry on the boundary torus. We also study the relation between the
3d-2d coupled partition function of our model and three dimensional holomorphic
blocks.
