Who is accused of committing the murder and why?
From your question, I am assuming that you are referring to the murder of William Frankenstein. The answer: Justine Moritz is the one accused of committing the crime.
In the story, Justine stands accused after a servant finds a picture of Victor's mother in her clothes while she is convalescing from an illness. Before William died, the young boy supposedly had the picture of Victor's mother on his person. When his corpse was discovered, however, the picture was missing. So, when the servant discovers the picture in one of Justine's dresses, she immediately takes the miniature portrait to another servant. The second servant then approaches the magistrate with the discovery, and this leads to Justine's arrest for William's murder.
Victor and Elizabeth both believe that Justine is innocent but are unable to save the poor young woman. They plead before the judges for her sake, but the men remain convinced that Justine is the killer. In the end, Justine confesses to William's murder because her confessor (priest) pressures her to do so. To get her to confess, the priest threatened her with excommunication and the fires of hell. Justine's confession, although false, brings her peace, as she sincerely believes that it will save her from "ignominy and perdition."
Meanwhile, Victor remains convinced that his "unhallowed arts" is the reason for Justine and William's deaths.
Justine Moritz who had been adopted by the Frankenstein family after being abandoned by her mother, was accused of killing William, Victor's younger brother. A locket that William had was found in Justine's pocket and she had slept outside of the town walls the after William was killed. Although she is innocent, she admitted to the murder because the priest threatened her with hell if she did not admit to the crime. Victor is sure the murder was actually committed by the monster, yet he says nothing about its creation and really does nothing to save Justine. His justification is:
"I was absent when it was committed, and such a declaration would have been considered as the ravings of a madman and would not have exculpated her who suffered through me."
Because of her confession, she is hanged for the murder, much to the distress of both Elizabeth and Victor.