Police piloting is done differently in different countries. In the USA many (most) pilots who fly for the police are police officers I understand. In some cases, the police train police officers to fly.
In the UK it is different. Police pilots are already experienced pilots before they start to fly for the police. Many are ex-military but they are civlians (in police terms). The CAA specifies a significant amount of relevant experience, which is usually comfortably exceeded by successful candidates. There were one or two accidents back in the early stages of police aviation in the UK- blamed on inexperienced pilots and pilots not concentrating on flying the aircraft. This is one of the reasons why the CAA make these requirements.
Although still in the minority, more civi trained pilots are employed to work for the police as time goes on, and the supply of ex-military guys is limited. It took me 10 years to get a police job, from when I started flying helicopters. Unless you are able to get the Queen to pay to teach you to fly, it will cost a bundle of time, effort and money BUT I can't think of anything I would rather do...........