  Unimodular gravity is a modified theory with respect to general relativity by
an extra condition that the determinant of the metric is fixed. Especially, if
the energy-momentum tensor is not imposed to be conserved separately, a new
geometric structure appears with potentially observational signatures. In this
paper, we study tidal deformability of compact star in the unimodular gravity
under the assumption of non-conserved energy-momentum tensor. Both the
electric-type and magnetic-type quadrupole tidal Love numbers are calculated
for neutron stars with polytrope model. It is found that the electric-type
tidal Love numbers are monotonically increasing, but the magnetic-type ones are
decreasing, with the increase of the non-conservation parameter. Compared with
the observational data from detected gravitational-wave events, a small
negative non-conservation parameter is favored.
