  The NA62 experiment recorded a large sample of $K^+ \rightarrow \mu^+
\nu_{\mu}$ decays in 2007. A peak search has been performed in the
reconstructed missing mass spectrum. In the absence of a signal, limits in the
range $2 \times 10^{-6}$ to $10^{-5}$ have been set on the squared mixing
matrix element $|U_{\mu4} |^2$ between muon and heavy neutrino states, for
heavy neutrino masses in the range 300-375 MeV/$c^2$. The result extends the
range of masses for which upper limits have been set on the value of $|U_{\mu4}
|^2$ in previous production search experiments.
