  In this article, we study the problem of the existence and nonexistence of
warping function associated with constant scalar curvature on pseudo-Riemannian
Poisson warped product space under the assumption that fiber space has constant
scalar curvature. We characterize the warping function on Einstein Poisson
warped space by taking the various dimensions of base space $B$ (i.e; (1). $dim
B=1,$ (2). $dim B=2,$ (3). $dim B\geq3$).
