  We report on the first measurement of the direct $CP$-violating asymmetry
($\mathcal{A}$) in the charmless decay $B^0 \to K^0\pi^0$ at Belle II and an
updated measurement of its branching fraction ($\mathcal{B}$). We use a sample
of electron-positron collisions collected in 2019 and 2020 at the
$\Upsilon(4S)$ resonance and corresponding to $62.8$ $\text{fb}^{-1}$ of
integrated luminosity. We reconstruct and select about $50$ $B^0 \to K_S^0
\pi^0$ candidates, and we measure $\mathcal{A}_{{K^0\pi^0}} =
-0.40_{-0.44}^{+0.46} (\text{stat}) \pm 0.04 (\text{syst})$ and
$\mathcal{B}(B^0 \to K^0 \pi^0) = [8.5_{-1.6}^{+1.7} (\text{stat}) \pm 1.2
(\text{syst})] \times 10^{-6}$. This is the first measurement of $CP$ violation
in $B^0 \to K^0\pi^0$ decays reported by Belle II. The results agree with
previous determinations and show a detector performance comparable with the
best Belle results.
