  In this paper, we generalize the CR Obata theorem for the Kohn Laplacian to a
closed strictly pseudoconvex CR manifold with a weighted volume measure. More
precisely, we first derive the weighted CR Reilly's formula associated with the
weighted Kohn Laplacian and obtain the corresponding first eigenvalue estimate.
With its application, we obtain the CR Obata theorem in a closed weighted
Sasakian manifold.
