The Criminal Emergency will remain open during a specific period of time. Check the countdown in the event widget (left side of the game screen): it will appear before the event starts.
 
Tap on the red skull icon to know which criminals must be arrested and complete all the quests to do it! You will receive gems and extra cards as log as the event progresses! 
 
Since each event provides a new Legendary character for your regular precincts, each event should restart to achieve the proper challenges.
 
You will be able to win useful rewards depending on the prisoners you rehabilitate during the event. Every week you will have the opportunity to unlock very special characters!
 
Event card packs will give you some permanent upgrades and the possibility of unlocking the Elite Cap. This special card will provide your Twilight City with great advantages during the current event.
 
Managers purchased in your regular police stations won't work in the Criminal Emergency (only the no-ads will), but they will work forever in your permanent levels.