  We present here a study of the impact of a heavy neutrino (or heavy neutral
lepton) on leptonic and semileptonic kaon decays. We used a simplified model
consisting of 3 light neutrinos responsible for neutrino oscillations and a
heavy sterile neutrino. We found that it can lead to large deviations from the
Standard Model predictions for leptonic decays, in conflict with experimental
measurements of $K_{e2}$ and the lepton universality test $R_K$. This allows to
derive new constraints on the leptonic mixing for heavy sterile neutrinos. No
tension was found when considering the semileptonic decays. Finally, we point
out the potential of the decay $K_L \rightarrow \nu \nu$ as a clear signature
of physics beyond the Standard Model.
