Chromium antimonide has emerged as a key material platform for studying altermagnetism because of its simple binary composition, high Néel temperature, and semimetallic electronic structure. Here, we investigate electrical and thermal magnetotransport in single-crystalline CrSb using steady- and pulsed-magnetic fields up to 65 T, and complement these measurements with neutron diffraction and magnetization data. We confirm the compensated magnetic structure and observe a large nonsaturating magnetoresistance together with a pronounced nonlinear Hall response at low temperatures. Multicarrier modeling, supported by mobility-spectrum analysis, reveals coexisting electron- and holelike charge carriers with mobilities up to ~3000 cm²/Vs and shows that the number of transport channels that can be resolved strongly depends on the accessible magnetic-field range. Thermal-transport measurements further reveal a nonlinear thermal Hall response and a thermal conductivity substantially exceeding a simple Wiedemann-Franz law. The broadly similar field and temperature evolution of electrical and thermal transport point to a dominant electronic contribution, while the remaining deviations indicate additional heat-carrying channels.