The recently discovered kagome superconductors AV₃Sb₅ (A = K, Rb, Cs)  exhibit unusual charge-density-wave (CDW) order with time reversal and rotational symmetry breaking, which may be related to chiral loop current order. In order to clarify the origin of the nontrivial CDW order, it is essential to clarify the relationship between time-reversal symmetry breaking and nematicity. Here, we report on the nematic susceptibility of CsV₃Sb₅. We performed elastoresistance measurements in two different configurations (four-probe and Montgomery methods), from which we obtained the same results for elastoresistance coefficients with A_1g (symmetric) and E_2g (nematic) symmetries. Both elastoresistance coefficients exhibit a steep jump at T_CDW, reflecting the occurrence of a first-order phase transition at T_CDW. The E_2g elastoresistance coefficient corresponding to the nematic susceptibility is temperature-independent below T_CDW, indicating that the nematic state in CsV₃Sb₅ is not even-parity ferroic order (q ≠ 0). In contrast, the elastoresistance coefficient with symmetric A_1g symmetry shows a broad peak structure around 30 K, which may be related to an anomaly reported in other experiments such as non-reciprocal transport measurements.