Work Separations - General. No advance notice of termination or resignation is required.The form may be mailed to P.O. Box 13697, Austin, Texas. 78711-3697; faxed to (512) 463-5709; or delivered to the James Earl Rudder Office Building, 1019. Resignation. If you resign from the City, you must submit a written resignation to your supervisor, which will be placed in your permanent personnel file. You'll often need to submit a formal letter to HR that you are resigning. Customer: I have an employee who put in a two weeks notice(Texas). We accepted the resignation and made it effective immediately due to many factors. Schedule a meeting with your boss ASAP so you can get it done. Set up enough time to resign and review your transition plan and any other outstanding issues.