If you're on android you could try making sure you dont have any extra apps running in the background that you don't need. Go into your settings and stop the ones you know you dont need like mail, etc. Don't stop any system apps.
Widgets, live wallpaper, weather, it all adds up and CC needs all the memory it can get. Look in your running apps, some apps autostart even when your not using them, and you can disable that if you have a setting for it or a custom rom.
The game takes up 45mb of memory on android, 1 process and 4 services, which is a pretty hefty amount for an app, Even when you're not playing it still runs at 7.2mb. I believe it even accumulates data as you play that can be flushed occasionally.
You could also try clearing your data and cache for crime city whenever it acts up.
Or it could be a crap phone...
On ios same thing, i have restored my phone/ipod to stock and reinstalled on occasion and it does seem to help for a little while.
Good luck.
PS. There's definitely an error with the boss eveent on android. It gives an error when u defeat him and u don't get anything for it no weapon drops.
Send a support ticket.