After your termination is processed, you will no longer have access to your DOE accounts. Give a resignation letter stating you're resigning and your last date is whenever (at least 2 weeks).I was told I need to give the state one whole payperiod. Resignation Checklist. Persons admitted to the bar of the State of New York sometimes seek to resign as attorneys and counselors-at-law. As a City employee, you may often deal with companies in the private sector. There are different resignation forms and fees depending on whether the company is domestic or foreign and entity type. A resignation letter is a formal notice stating your intention to leave your job. It typically includes details like your last day and potential next steps. An atwill New York employee (most) can legally leave a job without two weeks notice.