If you are entitled to Medicare Part A (Hospital Insurance) at age 65, you should enroll, even if you are still working. This may help cover some of the costs that your Federal Employees Health Benefits (FEHB) plan may not cover, such as deductibles, coinsurance, and charges that exceed the plan's allowable charges.  There is no premium for Part A. The Medicare taxes you pay while working entitles you to Part A.   

There is normally no advantage to signing up for the Medicare Part B (Medical Insurance) if you are still working at age 65.   Upon retiring, you will have an 8-month special enrollment period to sign up for Part B, if you wish to enroll. 

The official U.S. Government Medicare & You Handbook provides detailed information on Medicare.  You can also view information on what Medicare covers and other important information on the Medicare website.