  We construct and classify the free $U(\mathbb{C}L_0\oplus
\mathbb{C}M_0\oplus\mathbb{C}Y_0)$-modules of rank $1$ over the
Schr\"{o}dinger-Virasoro algebra $\mathfrak{sv}(s)$ for $s=0$.Moreover, we show
that the class of free $U(\mathbb{C}L_0\oplus\mathbb{C}M_0)$-modules of rank
$1$ over the Schr\"{o}dinger-Virasoro algebra $\mathfrak{sv}(s)$ for
$s=\frac{1}{2}$ is nonexistent.
