No, such a rule set by the state would be a violation of the German Basic law. You can basically say that the human life is worth infinit under german law, you can't have three infinit that is more than one infinit. The only case where that does not apply are in situations where the soon to be killed put himself into that situation by endangering someone else (aka protecting a victim from a murderer).

As such, the trolly problem would probably say "If there is no way to avoide human death, just keep your path"

Edit: You can see that by the decision about a law that wanted to give the government the right to shoot down a plane that was kidnapped by terrorists. The constiutional court said there can't be a law that puts innocent peoples life in the plain beyond the life of innocent people in the sky-scraper. If they can have a minute longer to life, than their lifes are protected. That said, the constituional court said that a pilot that would shoot them down would be protected by an overconstitutional emergency.