  The semi-exclusive channel
$\nu_{\mu}+\textrm{CH}\rightarrow\mu^{-}\pi^{0}+\textrm{nucleon(s)}$ is
analyzed using MINERvA exposed to the low-energy NuMI $\nu_{\mu}$ beam with
spectral peak at $E_{\nu} \simeq 3$ 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
$\sigma(E_{\nu})$ is obtained over the range 1.5 GeV $\leq E_{\nu} <$ 20 GeV.
Results are compared to GENIE and NuWro predictions and to published MINERvA
cross sections for $\nu_{\mu}\textrm{-CC}(\pi^{+})$ and
$\bar{\nu}_{\mu}\textrm{-CC}(\pi^{0})$. 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 $p\pi^{0}$ invariant mass distribution
is obtained, and the decay polar and azimuthal angle distributions in the rest
frame of the $p\pi^{0}$ system are measured in the region of $\Delta(1232)^+$
production, $W < 1.4$ GeV.
