Sure! The only way to continue playing Small Town Murders from the point you left off on a new device is to connect your game on the old device to either Facebook (Android and iOS devices) or Apple ID (iOS devices only). Doing so will also save your progress! 

To connect, please tap the cogwheel button in the screen's upper right corner, select the ‘Sign in’ button, and then select an account you prefer to connect. Once there, just follow the instructions, and you’ll be good to go!

You can then play across multiple devices by signing in to the same account!