  We examined the properties of a sample of BATSE Gamma--Ray Bursts (GRBs)
comprising events which have indications of association with a supernova (SN),
some on the basis of indications of re--brightening in the optical afterglow
light curve, but in most cases based only on the `loose' temporal and
directional coincidence inferred from the cross correlation of catalogs.
Despite of the large uncertainties in the latter selection method, the temporal
and spectral analysis reveal three interesting statistical results when the
sample is compared with that of all the BATSE GRBs: the GRBs tentatively
associated with SNe are found to predominantly (in $\sim$ 80% of the cases)
have single-peaked light curves, a softer spectrum (i.e. low energy power law
index $\alpha \sim$ --1.5) and tend not to follow the Lag-Luminosity and
Isotropic Energy--Peak Energy correlations. These three independent statistical
properties point toward the existence of a significant number of
under-luminous,GRB 980425-like events constituting -- at least from an
observational point of view -- a tail or a separate class with respect to the
whole of the BATSE GRB events. The unusually high percentage of SN Ibc among
those identified by the catalog cross--correlation (factor $\sim 4$ higher than
expected from SN catalog statistics) reinforces the non-randomness of (some of)
the selected events.
