  We calculate the TeV-PeV neutrino fluxes of gamma-ray bursts associated with
supernovae, based on the observed association between GRB 030329 and supernova
SN 2003dh. The neutrino spectral flux distributions can test for possible
delays between the supernova and the gamma-ray burst events down to much
shorter timescales than what can be resolved with photons. As an illustrative
example, we calculate the probability of neutrino induced muon and electron
cascade events in a km scale under-ice detector at the South Pole, from the GRB
030329. Our calculations demonstrate that km scale neutrino telescopes are
expected to detect signals that will allow to constrain supernova-GRB models.
