  In this work we give an estimate of the neutrino flux that can be expected
from the microquasar Cyg X-3. We calculate the muon neutrino flux expected here
on Earth as well as the corresponding number of neutrino events in the IceCube
telescope based on the so-called hypersoft X-ray state of Cyg~X-3. If the
average emission from Cyg~X-3 over a period of 5 yr were as high as during the
used X-ray state, a total of 0.8 events should be observed by the full IceCube
telescope. We also show that this conclusion holds by a factor of a few when we
consider the other measured X-ray states. Using the correlation of AGILE data
on the flaring episodes in 2009 June and July to the hypersoft X-ray state we
calculate that the upper limits on the neutrino flux given by IceCube are
starting to constrain the hadronic models, which have been introduced to
interpret the high-energy emission detected by AGILE.
