Well, that depends on that person's RE Code (Re-entry code, found on the DD-214). If the discharge was actually an Entry Level Separation (as is usually the case), then yes. The only discharge code that precludes police service is a dishonorable discharge. That being said, this person needs to get him/herself OFF drugs because they're going to undergo a lot of urinalysis testing while they're pursuing a police career. There's a drug test at virtually every step of the process, and randomly throughout a policeman's career.