The aim of this paper is to investigate the static perfect fluid spacetime $$M^{4}\times _{f}\mathbb {R}$$ such that $$(M^4, g)$$ is a half conformally flat Riemannian manifold. We prove that $$(M^4, g)$$ is, in fact, locally isometric to a warped product manifold $$I\times _{\phi }N^{3}$$ where $$I\subset \mathbb {R}$$ and $$N^{3}$$ is a space form. Consequently, we make an analysis of the Fischer-Marsden conjecture for a 4-dimensional Riemannian manifold.