I heard that while dribbling the ball, if the ball rises above shoulder level then it is a turnover. I don't have any idea about this rule.
My personal opinion is that it's not an infraction. When you see infractions called because someone dribbles high it's mainly because they "carry" the ball (putting your hand on the bottom hemisphere of the ball while dribbling), or somehow stop the motion of the ball during the normal dribbling process.
I searched the USA Basketball Website
I did see an article titled "7 Basketball Rules Myths":
In the article #2 explains
A dribble that bounces above the dribbler's head is an illegal dribble violation.
Reality: There is no restriction as to how high a player may bounce the ball, provided the ball does not come to rest in the player's hand.
So I would say dribbling the ball above shoulder height is legal
You can dribble as high as you want to dribble as long as your hand stays on top of the basketball. If your hand ends up on the bottom of the basketball it is a carry and the opposing team is awarded the basketball.
"Palming" the ball is illegal...but no ref will call it.
Players like Junior Bridgeman and Darrel Griffith had hands so small that the only way they could dunk the ball was to "carry it" on their upturned palms then turn their hand over once they got to the rim. Griff was called Dr. Dunkenstein when he was still at Lousiville as he dunked the ball consistently. I knew Griff in Utah and we measured hands...my fingers were at least 3 inches longer than his! Remarkable!
So yeah.."dribbling the ball is illegal" as it requires one to carry or palm the ball. But then traveling and 3 seconds in the lane, rolling picks, any foul by MJ was NEVER called either.
A carry violation consist of...
1.Dribbling the ball over your shoulder. If you dribble above shoulder height u must let the ball come back down below shoulder height before touching it again.
2.When you place your palm under the ball in a hesitation attempt or pass attempt and then resume dribbling the ball.