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.
Do You Really Need to Write a Resignation Letter? Why Write a Resignation Letter? Do you really need to write a formal resignation letter? The short answer is that most of the time, no letter of resignation is necessary. Many people do believe that as an employee you need to formally resign from a job by writing a formal resignation letter to your current employer.