  In this paper, we put forward a connection between the self-interacting dark
matter and the Dirac nature of neutrinos. Our exploration involves a $Z_4
\otimes Z_4'$ discrete symmetry, wherein the Dirac neutrino mass is produced
through a type-I seesaw mechanism. This symmetry not only contributes to the
generation of the Dirac neutrino mass but also facilitates the realization of
self-interacting dark matter with a light mediator that can alleviate
small-scale anomalies of the $\Lambda {\rm CDM}$ while being consistent with
the latter at large scales, as suggested by astrophysical observations. Thus
the stability of the DM and Dirac nature of neutrinos are shown to stem from
the same underlying symmetry. The model also features additional relativistic
degrees of freedom $\Delta N_{\rm eff}$ of either thermal or non-thermal
origin, within the reach of cosmic microwave background (CMB) experiment
providing a complementary probe in addition to the detection prospects of DM.
