Currently (see [1]) if a state space system has eigenvalues at 0, it will return a scalar NaN for DC gain:

        except LinAlgError:
            # zero eigenvalue: singular matrix
            return np.nan

The shape of the return is addressed in #126.

It may be possible to do better here: one relatively expensive way would be to minreal each input output pair and evaluate the DC gain. This would allow finite and non-finite entries in the returned matrix, rather than all NaNs. I'm not sure how to decide on +inf or -inf instead of NaN: in C*inv(-A)*B, if we find some sort of inverse of A that has infs (this is not hard using, e.g., singular value decomposition), one could still potentially add or subtract infs when multiplying by C and B, so getting NaNs.

[1]