Bluetooth RN-42 BOB disconnect

I'm wondering how many connections I need to switch off or disconnect. In my project, I'll have a serial port connected to Sparkfun's Bluetooth modem RN-41, but the user can also opt to not use Bluetooth and connect via an 1/8" stereo jack. In this case case I need to disconnect power to the Bluetooth modem (Vcc). Would I need to disconnect the TX and RX lines also, or will the arduino's (pro mini) serial work fine to the stereo jack without disconnecting them? The Bluetooth in question: