We measure both nonlinear absorption and nonlinear refraction in a ${{\rm CH}_3}{{\rm NH}_3}{{\rm PbBr}_3}$CH3NH3PbBr3 single crystal using the Z-scan technique with femtosecond laser pulses. At 1000 nm, we obtain values of 5.2 cm/GW and ${+}{9.5} \cdot {{10}^{ - 14}}\;{{\rm cm}^2}/{\rm W}$+9.5⋅10-14cm2/W for nonlinear absorption and nonlinear refraction, respectively. The sign and magnitude of the observed refractive nonlinearity are reproduced well by the two-band model. Our results suggest that the large nonlinear refractive index measured in perovskite nanostructures cannot be explained by an intrinsically high bound-electronic nonlinear refractive index in this emerging material class but is possibly caused by free carriers or quantum confinement effects.