I suspect the answer is no, but I am not able to either prove it, or provide an example. In Katz and Lindell's book, it is only said that with a perfectly secret encryption scheme, the plain and ciphertext distributions are independent. But when I try to construct an example with a non-uniform ciphertext distribution, (using say, 4 plaintexts as a message space), I cannot devise a plaintext and key distribution such that the resulting ciphertext distribution is not uniform.
What I am getting wrong? (or can anyone provide such an example?)