Joana, before I graduated from university and changed to another job I was a police officer as well. I worked in the German police for about nine years, I also came out while I was working there. I did this all by writing e-mails to the fellow officers which I used to work with. In the end, it was easier as I expected. Although I agree it is a field which is pretty dominated by "masculine behaviour", my coming-out was well-accepted even by those officers of who I expected they would never accept me.
The only downside was that my superior almost immediately ordered that I wasn't allowed to carry my handgun anymore. I had to hand it in indefinitely. Moreover, I had to leave the patrol force but I was given free choice regarding my future working field in the indoor staff. This procedure is common for any German police officer who has been diagnosed with "mental illness". No further comment on that...
Al least I was given a full set of female uniform. I loved to wear that one.

And I still have it today because they did not want it back after I resigned.
My police ID card was changed after my name change became final. I also had to make a new photo for this one.
Until I changed my job, I worked as a legal assistant in the police happily for another two years.