Relay JZC-11F causes parallel circuit switch to fail

I am using an Arduino with Bluetooth to use it as a garage door opener. The garage door has an internal RF receiver and a set of remotes which work independently. There is a manual push button switch on the wall, which attaches to the garage door by just wire screwed in to terminals on the garage unit. I tested the theory that if i shorted these connectors the garage door opens (or closes). Based on this I created an Arduino circuit and triggered a Relay JZC-11F to basically short this. And this works, which is the good news. However, the push button switch on the wall doesnt work with the arduino circuit attached to the same terminals. If i remove the arduino circuit out of this then the push button switch works again. I dont have access to a multimeter to check if there is any voltage being passed across the switch.

The circuit for the arduino is here: MyHomeAutomation/GarageRemoteSchematics_bb.png at master · shashisadasivan/MyHomeAutomation · GitHub

Any clues / ideas as to what may be causing this?

The relay coil is rated 12V at 37.5ma. If you're using the Arduino's 5V you won't have enough power to switch it.