Nobles are completely above common Law
It is mentioned in Law, Justice & Criminals chapter of Sigmar's Heirs (pg. 27) that nobles only answer to the Electors (kind of province governors), which then answered directly to the Emperor. This means that any accusation from a lower rank citizen could be easily disregarded. Only another noble could accuse a noble of any crime, and only the Elector Counts could decide if the nobles under their wing were guilty of anything.
Each noble, from the smallest landholder to the greatest, is theoretically beholden to one above him, up to the Electors, who answer only to the Emperor. In turn, those above owe protection to those below. Thus, if the Emperor has a problem with the Duke of Niebelwald, he has to make his complaint through the Elector of Averland, whose vassal the Duke is.
Not only that, but the Electors had the power to decide to ignore any Imperial decision they didn't like, which meant that unless the Emperors were in good terms with them, he couldn't get anything done or approved. The Electors are those who pick a new Emperor and had absolute power over justice within their domains. So, their power was absolute within their provinces.
As noted on the Law, Justice & Criminals chapter (pg. 27), nobles could bring a death sentence to any citizen below their rank:
The word of a noble often brings down a death sentence, whilst the unwritten rules of the thieves’ guilds are an unseen influence upon criminals and victims alike.
Their authority could sometimes defy the Inquisition's witch hunters:
The writ of a witch hunter supersedes any local authorities, though a powerful noble or clergyman may be able to defy them in a case of jurisdiction.
In Bretonnia it's a little different
The chapter Law & Justice of Knights of the Grail (pg.30) opens with this quote:
“There’s one law for the nobles, another for the rich, and another for the poor. We don’t bother learning the last because the poor cannot pay us.” - Louis Chamignon (nee Louise), L’Anguille lawyer
And describes how nobles are above peasants, even those of another lord:
A noble has a legal duty to protect, guide, and judge the peasants under his rule, but quite a lot is permitted under the guise of “instilling proper respect for the nobility,” and very few nobles bother to investigate reports of abuses. A noble who acts against another lord’s peasants is committing a crime against that noble but not against the peasants who are the actual victims.
But there are laws that apply to everyone in Bretonnia:
The royal laws forbid all standard crimes, such as theft, assault, and murder. Violence within the context of a legitimate grievance is permitted, however.
And laws that apply only to nobles:
The laws also forbid actions unbecoming to a noble, such as engaging in a trade.
Nobles may only go to trial if accused by someone of higher social position, normally only the King is above all the nobles, but there are nobles of a higher position that may act as judges for those nobles of lower position.
A court must be convened by the liege lord of the accused or by someone higher in the direct chain of fealty. The King, therefore, can convene a court to try any noble. The court must be publicly proclaimed three times on separate days, no more than two weeks before and no later than the day before. The convening lord sits as a judge, and seven other nobles of rank at least equal to the accused sit as a jury.
Their punishments, however, are hardly something to worry about:
Most sentences are symbolic; nobles are never subjected to imprisonment or corporal punishment. Fines are possible, but very rare, and mostly take the form of compensation. A noble who killed five of another noble’s servants in a drunken rage might be required to pay the costs of training replacements, for example. Common sentences include public apologies, specific services to the victim, particular limits on behaviour, or imposed quests of valour. In extreme cases, a court may petition the King to strip the noble in question of his fiefs, or even of his nobility.