  In the general two Higgs doublet model (g2HDM) that has extra Yukawa
couplings, we analyze their New Physics (NP) contributions to kaon mixing
parameter $\varepsilon_K$, direct CP violation parameter
$\varepsilon^\prime/\varepsilon$, and rare $K^+ \to \pi^+\nu\bar\nu$, $K_L \to
\pi^0\nu\bar\nu$, and $K_{L, S} \to \mu^+ \mu^-$ decays. We study correlations
between these observables, and call special attention to a unique
complementarity of kaon mixing and rare $K\to \pi \nu\bar\nu$ decays in probing
the exotic Higgs mass spectrum of g2HDM. The importance of kaon physics in
probing NP vis-\`a-vis B physics is stressed. One unexpected feature we uncover
is the special sensitivity of $K^+ \to \pi^+\nu\bar\nu$ to TeV scale charged
Higgs boson.
