The Chromospheric Lyman-Alpha SpectroPolarimeter is a sounding rocket instrument designed to measure for the first time the linear polarization of the hydrogen Lyman-{α} line (121.6 nm). The instrument was successfully launched on 3 September 2015 and observations were conducted at the solar disc center and close to the limb during the five-minutes flight. In this article, the disc center observations are used to provide an in-flight calibration of the instrument spurious polarization. The derived in-flight spurious polarization is consistent with the spurious polarization levels determined during the pre-flight calibration and a statistical analysis of the polarization fluctuations from solar origin is conducted to ensure a 0.014% precision on the spurious polarization. The combination of the pre-flight and the in-flight polarization calibrations provides a complete picture of the instrument response matrix, and a proper error transfer method is used to confirm the achieved polarization accuracy. As a result, the unprecedented 0.1% polarization accuracy of the instrument in the vacuum ultraviolet is ensured by the polarization calibration.