Why might you still want to write a resignation letter? Many experts believe that writing a formal or even a basic resignation letter when you're leaving your current job helps make you seem more courteous and professional. However, the real reason to write a resignation letter is to create a paper trail documenting that you have given notice (if your employer requires two weeks notice or some other amount of notice) on a certain date, and to formally kick of the process should there be any legal hiccups (quite rare) with incorrectly processing your final paycheck and last day of benefits.
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.