In principle, German citizenship is the prerequisite for becoming a police officer in Germany. Police forces are categorised as civil servants, and as a general rule, one may only work as a public servant if he is a German citizen( in the sense of Article 116 of the Basic Law). But the state laws also have a say in the appointment of civil servants. In each federal state, there are different regulations on whether and when one can become a public servant without holding a German passport. Therefore, it may be that you can start police training under certain conditions, even if you do not have German citizenship. To find out more about the relevant rules and regulations in your federal state, check with the Police Union, your local police or www.polizeitest.de.
Depending on the level of service you are striving for, various school certificates are also required. Besides, you should have no criminal records, (in some federal estates) maintain a certain body size, and meet specific health criteria. If you meet all these prerequisites, you can register for an eligibility procedure ("Eignungsverfahren") at a police school ("Polizeischule" or "Polizeifachschule").