  The signals of the neutral top-pion $\pi^{0}_{t}$ at the first muon collider
(FMC) are discussed by calculating its contributions to the processes
$\mu^{+}\mu^{-}\longrightarrow b\bar{b}$ and $\mu^{+}\mu^{-}\longrightarrow
\bar{t}c$. We find that the contributions to the process
$\mu^{+}\mu^{-}\longrightarrow b\bar{b}$ are very small and the ratio of signal
over square root of the background ($S/\sqrt{B})$ is smaller than 0.2. However,
in most of the parameter space, the $\pi^{0}_{t}$ can generate 36 and up to 649
observable $\bar{t}c$ events at the FMC. The signals of the neutral top-pion
$\pi^{0}_{t}$ may be detected via the process $\mu^{+}\mu^{-}\longrightarrow
\bar{t}c$ at the FMC.
