  We searched for the $\mu^+\mu^-$ decay of a light vector gauge boson, also
known as dark photon, in the $e^+ e^- \to \mu^+ \mu^- \gamma_{\rm ISR}$ process
by means of the Initial State Radiation (ISR) method. We used 1.93~fb$^{-1}$ of
data collected by the KLOE experiment at the DA$\Phi$NE $\phi$-factory. No
structures have been observed over the irreducible $\mu^+ \mu^-$ background. A
90\% CL limit on the ratio $\varepsilon^2=\alpha^{\prime}/\alpha$ between the
dark coupling constant and the fine structure constant of $ 3\times
10^{-6}-2\times 10^{-7}$ has been set in the dark photon mass region between
519 MeV and 973 MeV. This new limit has been combined with the published result
obtained investigating the hypothesis of the dark photon decaying into hadrons
in $e^+ e^- \to \pi^+ \pi^- \gamma_{\rm ISR}$ events. The combined 90\% CL
limit increases the sensitivity especially in the $\rho-\omega$ interference
region and excludes $\varepsilon^2$ greater than $(13-2)\times 10^{-7}$. For
dark photon masses greater than 600 MeV the combined limit is lower than
8~$\times\, 10^{-7}$ resulting more stringent than present constraints from
other experiments.
