We compute the tidal disruption event (TDE) rate around local massive black holes (MBHs) with masses as low as 2.5 x 10(4) M-circle dot, thus probing the dwarf regime for the first time. We select a sample of 37 galaxies for which we have the surface stellar density profile, a dynamical estimate of the mass of the MBH, and 6 of which, including our Milky Way, have a resolved nuclear star cluster (NSC). For the Milky Way, we find a total TDE rate of similar to 10(-4) yr(-1) when taking the NSC in account, and similar to 10(-7) yr(-1) otherwise. TDEs are mainly sourced from the NSC for light (