In neutral medium, potassium permanganate (KMnO$_4$) oxidises manganese(II) salts such as manganese sulfate (MnSO$_4$) to MnO$_2$.
The reaction in neutral medium is:
\[
2 \text{MnSO}_4 + \text{KMnO}_4 \rightarrow 3 \text{MnO}_2 + \text{K}_2\text{SO}_4
\]
Here, KMnO$_4$ acts as an oxidizing agent, and in neutral or slightly alkaline conditions, it reduces to MnO$_2$. The manganese in MnSO$_4$ is in the +2 oxidation state, and it is oxidized to the +4 oxidation state in MnO$_2$.
Thus, the correct answer is MnO$_2$.