You will not be asked to take a drug test when you hand in you application, if by "application" you mean an application to be hired as a police officer. But before you are hired, you will definitely be asked to take a drug test. Many police departments will also ask about your drug use in the past few years as well. Some police departments will require offices to submit to random drug testing and nearly all will require drug testing of an officer who has been involved in a major event such as a shooting or even a car accident. Just because you may have used drugs years ago but not any longer will not normally exclude you from being considered for a police office position. The rules for an application for a civilian job in a police department are usually much more lenient.