Yes, you can install a Ring Alarm Contact Sensor on a casement window. When installing the Contact Sensor it is best to put it opposite the hinges and in a spot the window can open/close easily. You are able to to place both pieces in unique angles that fit your window, as long as they are never more than one inch apart when closed. Some neighbors with casement windows find it best to place the sensor pieces at an angle so the edges line up, but do not fit flush together. See the provided example below.
We know casement windows can be tricky. This GIF above shows a creative approach to mounting, but it's not recommended unless the Contact Sensor is very securely mounted to the screen (and won't fall off) and there's at least a 1/2 inch of clearance for the back of the sensor so you can easily replace the batteries when needed. The Ring Alarm Slim Magnet is also a great option to consider for more mounting options. Note: Always remember to close your casement window if it rains or snows. Contact sensors are intended for indoor use only and should not get wet, as water can damage the sensor.
Contact Sensor Install Testing Tip
The best way to confirm if the pieces are installed optimally is to open the window, if the green light flashes and there is a chirp noise (if chirps are enabled in your settings), you have it installed correctly.
For a variety of ways to mount your Contact Sensor on a casement window or any other type of unique doors or windows, check out this Ring Help Center article.