Should I ask for a job transfer in person or in writing?

It is best if you ask for a job transfer in person, although you may have a written copy of your request to hand out if you'd like a written record of the exchange on file. If you are granted the transfer, you will eventually need to discuss exit procedures with your HR representative and/or supervisor regardless, so it's best if you take the time to personally express your desire for a move. Do not get personal or unprofessional when requesting a job transfer, as it's possible your request will be denied or your supervisor's recommendation will play an important role in your ability to secure a new position.