Is it normal for a green cheek conure to sleep with their head backwards

[Elvis Presley]

When my green cheek conure sleeps while I pet him he likes to tuck his head behind him. I believe this is normal but I was wondering

 

[SailBoat]

It is not uncommon for a Parrot to choose to sleep in this position.
For a Parrot to sleep in this position while you are petting is a demonstration of high comfort /trust in you.