The Formula One legend was skiing 13 feet (four metres) away from the marked trail in the Alpine resort when he fell and hit his head on rocks just before New Year's Eve.
He has been in intensive care ever since the incident on December 29. Doctors are gradually bringing him out of sedation, a Schumacher family spokesperson has confirmed.
The decision by officials to close the case does not prevent his relatives from bringing a civil action. Patrick Quincy said the F1 champion had been moving at a normal speed for "a good skier" when he struck a rock. He was thrown 10.4 metres (34 feet) into the air before hitting his head on another boulder on landing.
Investigators have also ruled out any wrongdoing by the shop where he rented his skis or the makers of the equipment.
Last week the family issued a statement saying they "strongly believe' he will recover. They also stressed that the most important element of his recovery was not the speed, but that it took place in a "continuous and controlled way."
The 45-year-old sportsman's wife Corinna has been at his side with their children Gina, 16, and Mick, 14. She has been joined in her vigil by his father and brother Ralf, also a successful F1 driver.
Their statement said: "Michael's family would like to again express their sincere thanks for the continuous sympathy coming from all over the world. The good wishes they receive help the family and we are convinced they also help Michael, who still is in a waking up process."
"As often in such situation, no day is like the next. The family is thankful for ones understanding that they would not wish to disclose medical details in order to protect Michael's privacy.
"As assured from the beginning we will continue to communicate any decisive new information on Michael's health state.
"We are aware that the wake up phase can take a long time.
"The family continues to strongly believe in Michael's recovery and place all their trust in the doctors, nurses and nursing auxiliaries team."