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We present the first search for heavy neutral leptons (HNL) decaying into$\nu e^+e^-$ or $\nu\pi^0$ final states in a liquid-argon time projectionchamber using data collected with the MicroBooNE detector. The data wererecorded synchronously with the NuMI neutrino beam from Fermilab's MainInjector corresponding to a total exposure of $7.01 \times 10^{20}$ protons ontarget. We set upper limits at the $90\%$ confidence level on the mixingparameter $\lvert U_{\mu 4}\rvert^2$ in the mass ranges $10\le m_{\rm HNL}\le150$ MeV for the $\nu e^+e^-$ channel and $150\le m_{\rm HNL}\le 245$ MeV forthe $\nu\pi^0$ channel, assuming $\lvert U_{e 4}\rvert^2 = \lvert U_{\tau4}\rvert^2 = 0$. These limits represent the most stringent constraints in themass range $35<m_{\rm HNL}<175$ MeV and the first constraints from a directsearch for $\nu\pi^0$ decays.

Search for heavy neutral leptons in electron-positron and neutral-pion final states with the MicroBooNE detector