An alarm for a door is operable to generate an alarm signal when a rotary grip member of the door is rotated to a particular position, such as an unlocked position. The alarm comprises a housing having a strap retainer configured to receive and retain a strap to hold the housing to the rotary grip member. The alarm comprises a tilt switch for switching when the housing is tilted. Control circuitry is interconnected to the tilt switch and to an annunciator and is operable to activate the annunciator dependent on a state of the tilt switch.