  We report measurements of the branching fraction ($\mathcal{B}$) and direct
$CP$-violating asymmetry ($A_{CP}$) of the charmless decay $B^{0} \to K^0
\pi^0$ at Belle II. A sample of $e^{+} e^{-}$ collisions, corresponding to
$189.8 fb^{-1}$ of integrated luminosity, recorded at the $\Upsilon(4S)$
resonance is used for the first decay-time-dependent analysis of these decays
within the experiment. We reconstruct about 135 signal candidates, and measure
$\mathcal{B}(B^{0} \to K^{0} \pi^{0})= [11.0 \pm 1.2 (stat) \pm 1.0 (syst)]
\times 10^{-6}$ and $A_{CP} (B^{0} \to K^{0} \pi^{0})= -0.41_{-0.32}^{+0.30}
(stat) \pm 0.09 (syst)$.
