  We perform a first step analysis toward generalization of the classification
of N=4 linear quiver gauge theories by Gaiotto and Witten including
Chern-Simons interaction. For this we investigate minimal N=4 U(N_1)_k x
U(N_2)_{-k} Chern-Simons theories and their superconformal indices. In the
previous publication we analyzed the three-sphere partition function of the
theories, which implies that the theory is good/ugly/bad if k-N_1-N_2 is
greater than/equal to/smaller than -1. In this paper we verify that this
classification is consistent with the behavior of the superconformal index. We
compare the superconformal indices for several pairs of non-bad theories
connected by the Hanany-Witten transition and confirm their coincidence up to
the contribution of one hypermultiplet.
