We report measurements of the linear polarization degree (PD) and angle (PA) for hard X-ray emission from the Crab pulsar and wind nebula. Measurements were made with the XL-Calibur (similar to 15-80 keV) balloon-borne Compton-scattering polarimeter in July 2024. The polarization parameters are determined using a Bayesian analysis of Stokes parameters obtained from X-ray scattering angles. Well-constrained (similar to 8.5 sigma) results are obtained for the polarization of the similar to 19-64 keV signal integrated over all pulsar phases: PD = (25.1 +/- 2.9) per cent and PA = (129.8 +/- 3.2)degrees. In the off-pulse (nebula-dominated) phase range, the PD is constrained at similar to 4.5 sigma and is compatible with the phase-integrated result. The PA of the nebular hard X-ray emission aligns with that measured by IXPE in the 2-8 keV band for the toroidal inner region of the pulsar wind nebula, where the hard X-rays predominantly originate. For the main pulsar peak, PD = (32.8(-28.5)(+18.2)) per cent and PA = (156.0 +/- 21.7)degrees, while for the second peak (inter-pulse), PD = (0.0(-0.0)(+33.6)) per cent and PA = (154.5 +/- 34.5)degrees. A low level of polarization in the pulsar peaks likely does not favour emission originating from the inner regions of the pulsar magnetosphere. Discriminating between Crab pulsar emission models will require deeper observations, e.g. with a satellite-borne hard X-ray polarimeter.