Polarization properties of coherent X-radiation produced by 72 MeV electrons interacting with a silicon monocrystal have been investigated experimentally at the superconducting Darmstadt linear accelerator S-DALINAC. Spatially resolved measurements of the direction and the degree of linear polarization show good agreement with expectations based on the kinematical theory of coherent polarization radiation and rule out a quasi-Cerenkov nature of this radiation.