Yes, you can. Sign-in to the same iCloud account and make sure that iCloud synchronization is turned on on both devices. If this is your case, but the game accounts are still different, please do the following:
1. Go to iOS Settings > iCloud and tap "Sign Out" on both devices.
2. Log back into the Apple account on the device with the game progress you want to use (#1).
3. Launch C.A.T.S. on device #1.
4. Make sure iCloud synchronization is turned on in game Options.
5. Log into the same Apple account on another device (#2).
6. Launch C.A.T.S. on the device #2.
7. Progress restoration message should pop up. Tap "Yes."
If you are still unable to play on another device under the same account, please check all cloud save settings and make sure that it is enabled on both devices. Also, check whether it is possible to restore the progress on some other iOS device besides the one you try to transfer progress to.
If you prefer, you may also use Facebook for this purpose. Just go to the game settings and connect your Facebook to both accounts. When progress restoration message pops up, tap "Yes." You are all set!