  Using $J/\psi$ radiative decays from 9.0 billion $J/\psi$ events collected by
the BESIII detector, we search for di-muon decays of a $CP$-odd light Higgs
boson ($A^0$), predicted by many new physics models beyond the Standard Model,
including the Next-to-Minimal Supersymmetric Standard Model. No evidence for
the $CP$-odd light Higgs production is found, and we set $90\%$ confidence
level upper limits on the product branching fraction $\mathcal{B}(J/\psi \to
\gamma A^0)\times \mathcal{B}(A^0 \to \mu^+\mu^-)$ in the range of
$(1.2-778.0)\times 10^{-9}$ for $0.212 \le m_{A^0} \le 3.0$ GeV/$c^2$. The new
measurement is a 6-7 times improvement over our previous measurement, and is
also slightly better than the BaBar measurement in the low-mass region for
$\tan \beta =1$.
