  We report the first experimental upper bound to our knowledge on possible
in-matter torsion interactions of the neutron from a recent search for parity
violation in neutron spin rotation in liquid He-4. Our experiment constrains a
coefficient $\zeta$ consisting of a linear combination of parameters involving
the time components of the torsion fields $T^\mu$ and $A^\mu$ from the nucleons
and electrons in helium which violates parity. We report an upper bound of
$|\zeta|<9.1x10^{-23}$ GeV at 68% confidence level and indicate other physical
processes that could be analyzed to constrain in-matter torsion.
