The dielectric constant and the correlation function of a system of sticky hard spheres with an embedded point dipole is calculated at different densities, temperatures and dipole moments using the LHNC and LIN approximations. Comparison between these theories and with the dielectric constant of hard dipolar spheres are presented. It is found that LIN values are lower than LHNC ones and that the theories predict opposite trends for the dielectric constant when the stickiness is included. An analysis of this discrepancy is given.