My budgies seem to sleep attached to the side of cage or upside down on the roof of the cage

 

Amazing....I was never aware of this

 

 

Also, in the morning when i remove the sheet from over the cage they let me rub their bellies...is this because they are still sleepy??? Even though their eyes are open

I seem to have a similar problem to you, one of my budgies that I bred sleeps upside down on th ceiling and is in love with her dad....

She's an odd one-just like her dad (:

Mine use to do this too, and Koko still does. I was trying to figure out what caused this, but all I could see was that they reacted to how long I was gone, lighting, and the time of night. If I left the light on when their cage was covered for the night, and left the room for a long period of time, they would be like that when I came back. But when I got in the room, they would go back to their perches and start acting normal again. I wonder why?

When I was looking after a budgie for someone, I woke up in the night occasionally to see a dark shape inside the cage hanging from the roof . When I came put the torch on, it turned out to be a budgie! Weird.

i have some budgies that seem to sleep on the wire, but most sleep on the perches. Nothing but personal choice involved.