  Let $X=(X_t, t\geq 0)$ be a superprocess in a random environment described by
a Gaussian noise $W^g=\{W^g(t,x), t\geq 0, x\in \mathbb{R}^d\}$ white in time
and colored in space with correlation kernel $g(x,y)$. We show that when $d=1$,
$X_t$ admits a jointly continuous density function $X_t(x)$ that is a unique in
law solution to a stochastic partial differential equation
  \begin{align*} \frac{\partial }{\partial t}X_t(x)=\frac{\Delta}{2}
X_t(x)+\sqrt{X_t(x)} \dot{V}(t,x)+X_t(x)\dot{W}^g(t, x) , \quad X_t(x)\geq 0,
\end{align*} where $V=\{V(t,x), t\geq 0, x\in \mathbb{R}\}$ is a space-time
white noise and is orthogonal with $W^g$. When $d\geq 2$, we prove that $X_t$
is singular and hence density does not exist.
