The semi-exclusive channel $ u_{mu}+textrm{CH}rightarrowmu^{-}pi^{0}+textrm{nucleon(s)}$ is analyzed using MINERvA exposed to the low-energy NuMI $ u_{mu}$ beam with spectral peak at $E_{ u} simeq 3$ GeV. Differential cross sections for muon momentum and production angle, $pi^{0}$ kinetic energy and production angle, and for squared four-momentum transfer are reported, and the cross section $sigma(E_{ u})$ is obtained over the range 1.5 GeV $leq E_{ u} <$ 20 GeV. Results are compared to GENIE and NuWro predictions and to published MINERvA cross sections for $ u_{mu}textrm{-CC}(pi^{+})$ and $bar{ u}_{mu}textrm{-CC}(pi^{0})$. Disagreements between data and simulation are observed at very low and relatively high values for muon angle and for $Q^2$ that may reflect shortfalls in modeling of interactions on carbon. For $pi^{0}$ kinematic distributions however, the data are consistent with the simulation and provide support for generator treatments of pion intranuclear scattering. Using signal-event subsamples that have reconstructed protons as well as $pi^{0}$ mesons, the $ppi^{0}$ invariant mass distribution is obtained, and the decay polar and azimuthal angle distributions in the rest frame of the $ppi^{0}$ system are measured in the region of $Delta(1232)^+$ production, $W < 1.4$ GeV.
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