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We report the magnetocapacitance effect and the magnetostriction in the spin-crossover (SCO) complex [MnIII(taa)] (H3taa = tris(1-(2-azolyl)-2-azabuten-4-yl)amine). It is shown that huge enhancements of dielectric constant and lattice volume are caused by the field-induced SCO transition from the low-spin to the high-spin states in [MnIII(taa)]. In addition, the temperature-field phase diagram of the field-induced SCO in thermal equilibrium state is clarified up to 28 T. Our analysis suggests that a large magnetocaloric effect can also be caused by the field-induced SCO. These results indicate the possibility of multiple control of various material properties by the field-induced SCO.