  We study the influence of a possible H dibaryon condensate on the equation of
state and the overall properties of neutron stars whose population otherwise
contains nucleons and hyperons. In particular, we are interested in the
question of whether neutron stars and their masses can be used to say anything
about the existence and properties of the H dibaryon. We find that the equation
of state is softened by the appearance of a dibaryon condensate and can result
in a mass plateau for neutron stars. If the limiting neutron star mass is about
that of the Hulse-Taylor pulsar a condensate of H dibaryons of vacuum mass 2.2
GeV and a moderately attractive potential in the medium could not be ruled out.
On the other hand, if the medium potential were even moderately repulsive, the
H, would not likely exist in neutron stars. If neutron stars of about 1.6 solar
mass were known to exist, attractive medium effects for the H could be ruled
out. Certain ranges of dibaryon mass and potential can be excluded by the mass
of the Hulse-Taylor pulsar which we illustrate graphically.
