Lego's "My City" game includes police gameplay, and can be downloaded for smartphones. It is a free game, so it does not require a purchase. "My City" is available from iTunes, Google Play, the Amazon Appstore and Samsung Apps.
"My City" includes fire fighting, racing, cargo helicopter and water rescue elements as well as police chases. It contains 12 different mini-games. All content in the game is free and included in the initial download; there are no in-app purchases. The game does not contain any advertising and is rated as appropriate for children ages 4 and up by Apple's iTunes store.