Chameleon sleeping

You can add more sticks and plants/ branches to your enclosure. Maybe check you heat levels and humidity. Because even though some just like to hang out on screens, sometimes they are looking for a warmer area or a cooler area or an area with less or more humidity. So I would first have someone do a husbandry check and take it from there.
 
If she's still of a size that she can climb around on the screen while she's awake, chances are very slim that she'd fall when sleeping. These animals are expert at clinging onto branches and twigs while they sleep—even in inclement weather.

When they get older, some chameleons forgo much screen climbing because their claws grow to a point that they don't fit as easily into the holes in the mesh. More likely she'd fall during this transitional phase, but they're built to withstand falls from much higher heights.

https://www.chameleonforums.com/threads/chameleon-fall.14071/
 
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