  We present the first results from the STAR MTD of mid-rapidity charmonium
measurements via the di-muon decay channel in p$+$p, p$+$Au, and Au$+$Au
collisions at $\sqrt{s_{_{\rm NN}}}=200$~GeV at RHIC. The inclusive $J/\psi$
production cross section in p$+$p collisions can be described by the
Non-Relativistic QCD (NRQCD) formalism coupled with the color glass condensate
effective theory (CGC) at low transverse momentum ($p_T$) and next-to-leading
order NRQCD at high $p_T$. The nuclear modification factor in p$+$Au collisions
for inclusive $J/\psi$ is below unity at low $p_T$ and consistent with unity at
high $p_T$, which can be described by calculations including both nuclear PDF
and nuclear absorption effects. The double ratio of inclusive $J/\psi$ and
$\psi(2S)$ production rates for $0<p_T<10$~GeV/$c$ at mid-rapidity between
p$+$p and p$+$Au collisions is measured to be 1.37~$\pm$~0.42~$\pm$~0.19. The
nuclear modification factor in Au$+$Au collisions for inclusive $J/\psi$ shows
significant $J/\psi$ suppression at high $p_T$ in central collisions and can be
qualitatively described by transport models including dissociation and
regeneration contributions.
