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.
Spot the Signs. Do you have a good relationship with your manager? Is he or she relatively reasonable? Do you have regular one_on_ones where you talk about your career goals and growth? If so, it's likely that your boss will accept your resignation with grace, help develop a plan of action for your last two weeks, and maybe even attend your farewell happy hour.