  We are investigating universal relations between different normalisations of
the moment of inertia and the compactness of neutron stars in slow rotation
approximation. We study the relations in particular class of massive
scalar-sensor theories with self-interaction, for which significant deviations
from General Relativity are allowed for values of the parameters that are in
agreement with the observations. Moment of inertia-compactness relations are
examined for different normalisation of the moment of inertia. It is shown that
for all studied cases the deviations from EOS universality are small for the
examined equations of state. On the other hand the scalarization can lead to
large deviations from the general relativistic universal relations for values
of the parameters that are in agreement with the current observations that can
be potentially used to set further test the scalar-tensor theories.
