Transition from Computer Science to Statistics
I think it depends on which country you want to apply for the Grad School. In Japan, you have a very Math oriented entrance examination for the Math department, and is usually the most important factor that decides whether you get in or not.

In USA, the educational system is different, since Undergrad education is often not oriented to a specific area, and you have a good chance as long as you get a high GRE score and have a good set of Recommendation letters (preferably from the Dean of your Univ. if you are not from the US).

As an example, take a look at Stanford's admission requirements:

International Academic Credentials

For India, you do need some kind of engineering background, but other countries like Japan, can in theory apply as long as they have finished an undergrad regardless the discipline.

Bear in mind though, that a PhD in statistics has a hefty load of subjects that assume that you have some mastery on math and advanced math(which, to be honest, the GRE does not cover). So you might have to throw in some hours just to level even with the rest of the students that have math undergrads.