  We report the results of a neutrino search in Super-Kamiokande for coincident
signals with the first detected gravitational wave produced by a binary neutron
star merger, GW170817, which was followed by a short gamma-ray burst,
GRB170817A, and a kilonova/macronova. We searched for coincident neutrino
events in the range from 3.5 MeV to $\sim$100 PeV, in a time window $\pm$500
seconds around the gravitational wave detection time, as well as during a
14-day period after the detection. No significant neutrino signal was observed
for either time window. We calculated 90% confidence level upper limits on the
neutrino fluence for GW170817. From the upward-going-muon events in the energy
region above 1.6 GeV, the neutrino fluence limit is $16.0^{+0.7}_{-0.6}$
($21.3^{+1.1}_{-0.8}$) cm$^{-2}$ for muon neutrinos (muon antineutrinos), with
an error range of $\pm5^{\circ}$ around the zenith angle of NGC4993, and the
energy spectrum is under the assumption of an index of $-2$. The fluence limit
for neutrino energies less than 100 MeV, for which the emission mechanism would
be different than for higher-energy neutrinos, is also calculated. It is $6.6
\times 10^7$ cm$^{-2}$ for anti-electron neutrinos under the assumption of a
Fermi-Dirac spectrum with average energy of 20 MeV.
