However, at most companies, there's no formal requirement that you do so. Most employment in the United States is called "at will", which means that your current employer can fire you at any time and for any reason (except those that are prohibited under law).
State Your Intent. The whole theme of your resignation letter is the statement that, well, you resign. You don't need to play coy__the time has passed for you to fish around for a counteroffer if it's gotten this far. At this point, you've made your decision to leave, and this letter needs to reflect that.