While Gaussian signalling is assumed in many studies on covert communications, its optimality has not been carefully investigated. In this work, we examine this optimality by considering the approach of upper bounding D(p₀ (y)∥p₁ (y)) as the covert communication constraint, where D(p₀(y)∥p₁(y)) is the Kullback-Leibler divergence from p₀ (y) to p₁(y), p₀(y) and p₁ (y) are the likelihood functions of the observation y at the warden under the null hypothesis (no covert transmission) and alternative hypothesis (a covert transmission occurs), respectively. Considering additive white Gaussian noise at both the receiver and the warden, we prove that Gaussian signalling is not optimal in terms of maximizing the mutual information of transmitted and received signals for covert communications with D(p₀(y)∥p₁ (y)) ≤ 2ϵ² as the constraint. We also explicitly show a skew-normal signalling can outperform Gaussian signalling in terms of achieving higher mutual information subject to the same covertness constraint D(p₀(y)∥p₁ (y)) ≤ 2ϵ².