Even if you're not close with your boss, chances are you have a working, first_name_basis relationship. Maintaining that in your official letter is okay. You don't need to keep a Victorian level of formality here__just make sure it's a professional tone.
Turning in your two weeks notice can be terrifying__because no matter how well you think you know your supervisor, you can never be 100% sure of his or her reaction. Will he be furious and insist on walking you out the door immediately? Will she beg you to stay, enticing you with an enormous raise? Or will he be completely civil and wish you the best of luck?