$P{D}_4$-complexes with ${\pi }_2$ a projective $\mathbb{Z}[{\pi }_1]$-module

Let $X$ be a $P{D}_4$-complex and let $\pi ={\pi }_1(X)$. If $\pi$ is torsion-free and ${\pi }_2(X)$ is a finitely generated projective $\mathbb{Z}[\pi ]$-module then either $\pi$ is free or $\pi$ is $FP$ and $c\mathrm{.}d\mathrm{.}\pi =4$. If, moreover, $H^3(\pi ;\mathbb{Z}[\pi ])=0$ then $\pi$ is a free product of $P{D}_4$-groups and a free group.