We present optical diagnostics of the sample of local (z ≤ 0.1) Host Galaxies (HG) of long duration Gamma-Ray Burst (LGRB) with associated supernova available to date. In particular we revisit the HG031203 using a set of spectra acquired with VLT. Taking into account the Galactic colour excess E MW(B - V) = 0.72 mag in the direction of the burst, we derive for this galaxy an intrinsic reddening E(B - V) HG ≈ 0.4 mag. With EW rest(Hα) = 757Å and SFR(Hα) = 12.3 ± 2.1 M ⊙yr -1, this system is likely to be undergoing a very intense burst of star formation. Furthermore, after investigating for traces of Wolf-Rayet (WR) stars emission in HG031203 spectra, we conclude that this galaxy does not host a clearly detectable WR population. Finally, we compare the properties of local LGRB hosts, with those of a complete sample of 1029 Emission Line Galaxies (ELGs) with z ≤ 0.1 from the KPNO International Spectroscopic Survey (KISS). We find that HGs are characterized by a specific star formation rate (SSFR) higher than normal.