Ralf Schumacher has been allowed to leave hospital and return home to Austria following a heavy crash at Sunday's U.S. Grand Prix, his Formula One team BMW-Williams said on Monday.

But doubts remain over the German's participation in the July 4 French Grand Prix following the accident at Indianapolis after Williams said he would not take part in testing this week.

"After examination by medical staff this morning, he has been discharged and is flying home to Salzburg early this afternoon (local time)," Williams said in a statement.

"Ralf is well, but has a bruised back and strained back muscles. He will not be taking part in scheduled testing duties for the team due to commence on Wednesday in Jerez."

Schumacher crashed on the fastest part of the course at Indianapolis, spinning on the banking at turn 13 where speeds reach around 320 kph and slamming backwards into the wall before coming to a stop in the middle of the track.

Medical staff spent more than 10 minutes gingerly extricating him from the shattered car before taking him to hospital for precautionary checks.

Also Read Barrichello to challenge Schumi Schumi wins US Grand Prix

Tyre supplier Michelin said a punctured tyre caused the crash following damage by debris from an earlier four-car collision.

Mario Theissen, motorsport director of Williams's engine partners BMW, said that there were doubts about Schumacher's presence on the starting grid at Magny-Cours.

"There is clearly a question mark (about his participation)," said Theissen. "I cannot tell what it will be but it has to be his own decision."

Last September, Schumacher missed the Italian Grand Prix at Monza after a similar high-speed crash in testing at the circuit left him struggling to overcome concussion.

Williams's former technical director Patrick Head, now elevated to head of engineering, recently suggested that Schumacher had been still suffering the after-effects of that crash well into the new season.

Williams have an official reserve driver in Spaniard Marc Gene, who is eager to be considered as a replacement for departing Colombian Juan Pablo Montoya and stood in for Schumacher last year.