An extension of a model of neutrino masses to the quark sector provides an interesting link between these two sectors. A parameter which is important to describe neutrino oscillations and masses is found to be a crucial one appearing in various "penguin" operators, in particular the so-called Z penguin. This parameter is severely constrained by the rare decay process K-L --> mu(+) mu(-). This in turn has interesting implications on the decay rates of other rare processes such as K-L --> mue, etc., as well as on the masses of the neutrinos and the masses of the vectorlike quarks and leptons which appear in our model.