  In the simplest scheme for neutrino masses invoking a triplet of Higgs
scalars there are two CP-even neutral Higgs bosons $H_i$ (i=1,2) and one
massive pseudoscalar $A$. For some choices of parameters, the lightest $H_1$
may be lighter than the Standard Model Higgs boson. If the smallness of
neutrino mass is due to the small value of the triplet expectation value, as
expected in a seesaw scheme, the Higgs bosons may decay dominantly to the
invisible neutrino channel. We derive limits on Higgs masses and couplings that
follow from LEP I precision measurements of the invisible Z width.
