To remove a car radio from its console in the dashboard, you may or may not have to remove the battery as well. It all depends on whether or not you have removed the power source from the radio so you do not get shocked. Should you not wish to remove the car battery you can remove the fuse to the radio to turn off the power to the radio. If you do not know where the fuse is or how to remove it, then your best bet is to remove the battery prior to removing the radio to prevent shock.
For more info, see Car Stereo Installation: A How To Guide