  We present the results for a search of high-energy muon neutrinos with the
IceCube detector in coincidence with the Crab nebula flare reported on
September 2010 by various experiments. Due to the unusual flaring state of the
otherwise steady source we performed a prompt analysis of the 79-string
configuration data to search for neutrinos that might be emitted along with the
observed gamma-rays. We performed two different and complementary data
selections of neutrino events in the time window of 10 days around the flare.
One event selection is optimized for discovery of E^-2 neutrino spectrum
typical of 1st order Fermi acceleration. A similar event selection has also
been applied to the 40-string data to derive the time-integrated limits to the
neutrino emission from the Crab. The other event selection was optimized for
discovery of neutrino spectra with softer spectral index and TeV energy
cut-offs as observed for various galactic sources in gamma-rays. The 90% CL
best upper limits on the Crab flux during the 10 day flare are 4.73 x 10^-11
cm-2 s-1 TeV-1 for an E^-2 neutrino spectrum and 2.50 x 10^-10 cm-2 s-1 TeV-1
for a softer neutrino spectra of E-2.7, as indicated by Fermi measurements
during the flare. IceCube has also set a time-integrated limit on the neutrino
emission of the Crab using 375.5 days of livetime of the 40-string
configuration data. This limit is compared to existing models of neutrino
production from the Crab and its impact on astrophysical parameters is
discussed. The most optimistic predictions of some models are already rejected
by the IceCube neutrino telescope with more than 90% CL.
