Can you become a police officer with a general discharge from the military?

It depends entirely on the circumstances of the discharge, the number of applicants applying, the ratio of the number of applicants as compared to the number of available positions, and internal regulations of the department. Also bear in mind that different departments have different standards and different reasons for those standards. Long story short, if you have a general discharge from the military, be honest and upfront about it with the background investigator and apply to multipledepartments as to find the best mutual fit for you.