  We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field
theories. In a gauge theory the partition function is the sum of the
contributions of sectors specified by holonomies, and we should carefully
choose the relative signs among the contributions. We argue that the
factorization to holomorphic blocks is a useful criterion to determine the
signs and propose a formula for them. We show that the orbifold partition
function of a general non-gauge theory is correctly factorized provided that we
take appropriate relative signs. We also present a few examples of gauge
theories. We point out that the sign factor for the orbifold partition function
is closely related to a similar sign factor in the lens space index and the 3d
index.
