The car keys should always stay inside of the Zipcar at all times. The car keys should only be used to start and turn off the engine and you should use your Zipcard or mobile device to lock and unlock the doors.
In most cases, the keys are tethered to the steering wheel column but they may be in the center console as well. If the car has a push start button you can just put your foot on the brake and push the button. No need for a key.