The only time a shift cipher considers to be perfectly secure, is when used on a single letter of plaintext and no more. Having that in mind, we can say it is certainly not perfectly secure.
CeasarCaesar cipher is perfectly secret only in the special case with the assumption that 26 keys are used in equal probability. Suppose that we have a plaintext of 50 characters long, if each key for each character is chosen equiprobably then you end with 26^50 possible keys.
That is my answer, is it correct?