Modulation identification is an important part of wireless communications systems e.g., blind receivers can benefit. from the methods that can identify the modulation of the received signals without a priori information. Moreover, distinction of OFDM systems from single carrier systems is highly important for adaptive receiver design algorithms. OFDM signals exhibit Gaussian characteristics in time domain in contrast with the single carrier signals. However, when the wireless communications considered, Gaussianity of the received samples is affected from the channel impairments along with the frequency, phase offsets and sampling mismatch. In this paper, we analyzed how the time-domain Gaussianity of fourth order cumulants of OFDM signals is affected under these conditions. A general chi-square constant false alarm rate Gaussianity test which employs estimates of cumulants and their covariances is adapted to the specific case of OFDM signals. A parametric simulation analysis which investigates the performance of the proposed method by the changes in the parameters such as signal to noise ratio, number of symbols, and modulation order is provided. The performance of proposed method is compared with moment based tests as well.