Dash should automatically disconnect from the Bluetooth and the GPS after one minute of it knowing the vehicle is off to reduce the drain on your cell phone's battery. If that's not happening, please let us know at email@example.com.
In terms of your car's battery, the OBD-II interfaces will use some energy while plugged in. Most of these have some sort of sleep mode, but some of the generic OBD interfaces may slowly drain your car's battery. In general, it's a good idea to remove your OBD-II interface if it'll be more than a few days before your next drive.