As soon as the first time you go to register your twins for kindergarten, you will think about their class placements, perhaps even before that. The question will always be: together or separate classes? And the truth is, you the parent are the best person (along with your spouse) to answer this. The problem is that you often don't get the final decision. The school does.
However, you can help your chances by making the request in the best possible fashion.
Usually this will be in writing, and some schools won't consider it otherwise. So my advice is to write a concise letter to the school's principal or administrator, and if already in the school, cc it to the current classroom teacher or teachers. Keeping them informed is important because teachers often do the class placements. Don't cc the school board superintendent or supervisor. It could be looked on by the principal as challenging his or her authority. Give your reasons as clearly and succinctly as possible. If you wish to speak to the principal in person about class placements, request this in the letter.
The administrator may tell you that the school has a policy of separating twins. If so, ask to have it explained to you. It may just be a decision made at the administrator's discretion. If you want your twins together, and the school is insisting on separation, then at least ask that your twins be in adjacent or nearby classrooms to increase their comfort level. Good luck with your request. Be persistent, yet patient.