  Polarization of the >~400 keV hard tail of the microquasar Cygnus X-1 has
been independently reported by INTEGRAL/IBIS, and INTEGRAL/SPI and interpreted
as emission from a compact jet. These conclusions were, however, based on the
accumulation of all INTEGRAL data regardless of the spectral state. We utilize
additional INTEGRAL exposure accumulated until December 2012, and include the
AMI/Ryle (15 GHz) radio data in our study. We separate the observations into
hard, soft, and intermediate/transitional states and detect radio emission from
a compact jet in hard and intermediate states, but not in the soft. The 10-400
keV INTEGRAL (JEM-X and IBIS) state resolved spectra are well modeled with
thermal Comptonization and reflection components. We detect a hard tail in the
0.4-2 MeV range for the hard state only. We extract the state dependent
polarigrams of Cyg X-1, which all are compatible to no or undetectable level of
polarization except in 400-2000 keV range in the hard state where the
polarization fraction is 75$\pm$32 % and the polarization angle 40.0 +-14 deg.
An upper limit on the 0.4-2 MeV soft state polarization fraction is 70%. Due to
the short exposure, we obtain no meaningful constraint for the intermediate
state. The likely detection of a >400 keV polarized tail in the hard state,
together with the simultaneous presence of a radio jet, reinforce the notion of
a compact jet origin of the 400 keV emission.
