  Our previous analysis on the contributions of mirror matter admixtures in
ordinary hadrons to K_L to gamma gamma is extended to study the relevance of
such contributions to the K_L to mu^+ mu^- rare decay. The mixing angle of the
admixtures previously determined to describe the enhancement phenomenon in two
body non-leptonic decays of strange hadrons is used, along with recent results
for the description of the strong and electromagnetic interaction parts of the
transition amplitudes. We find that these admixtures give a significant
contribution with a small SU(3) breaking of only 2.8%, we also find a value of
\sim -17.9^{\circ} for the eta-eta' mixing angle consistent with some of its
determinations in the literature and a preferred negative value around -16 for
the local counter-term contribution chi_1 + chi_2 consistent with the existence
of a unique counter-term assuming lepton universality. We conclude that those
mixings may be relevant in low energy physics and should not be ignored.
