All-inorganic colloidal perovskite quantum dots (QDs) based on cesium, lead, and halide have recently emerged as promising light emitting materials. CsPbBr3 QDs have also been demonstrated as stable two-photon-pumped lasing medium. However, the reported two photon absorption (TPA) cross sections for these QDs differ by an order of magnitude. Here we present an in-depth study of the TPA properties of CsPbBr3 QDs with mean size ranging from 4.6 to 11.4 nm. By using femtosecond transient absorption (TA) spectroscopy we found that TPA cross section is proportional to the linear one photon absorption. The TPA cross section follows a power law dependence on QDs size with exponent 3.3 +/- 0.2. The empirically obtained power-law dependence suggests that the TPA process through a virtual state populates exciton band states. The revealed power-law dependence and the understanding of TPA process are important for developing high performance nonlinear optical devices based on CsPbBr3 nanocrystals.