We extend Hardy's theorem for rotation due to Lakey and Hogan for Dunkl transform associated with the reflection group (Formula presented.) in (Formula presented.) by using Dunkl-Hermite semigroup. In fact, we characterize (Formula presented.) by considering the decay of f and it's Dunkl transform (Formula presented.) along some lines in the complex plane, and we give a d-dimensional analogue for the same corresponding to the reflection group (Formula presented.) Moreover, we prove a version of Hardy's theorem, assuming the decay of Dunkl-Hermite coefficients. © 2020 Informa UK Limited, trading as Taylor & Francis Group.