Tei Sukone commited such a crime.
She had kidnapped Miku from her home and killed her. She then planted the severely mutilated body in Aokigahara forest to make it seem like a suicide. However, she didn't know that she had done such damage to the corpse that it didn't look like a suicide at all. Avanna had noticed this when she found Miku.
Detective Kagamine explained it all.
After Madam Aoki had been robbed, the investigators Akiko and Ia noted the silver hair that was found. Soon after, Haku Yowane had been murdered and the same hair was found. Detective Yuzuki had compared the swatches of hair, and they were the same.
Ia was Tei's only friend. She knew all about the plan, but didn't expect Tei to actually go through with it. She was in for a surprise when she heard of Miku Hatsune's disappearance. Ia said nothing, though. She still didn't think Tei would go through with the plan, and since the famous pop star did have a few haters she knew that it had to have been one of them instead.
After Avanna found the body, the autopsy was preformed and Dr. Cul and Dr. Merli reached the conclusion that it was indeed Miku Hatsune's corpse. They determined that Miku had been murdered, and there was DNA on some of her fatal wounds.
Soon, the three detectives had the DNA and basic police sketches of the murderer. They were undercover and searching, but hadn't gotten any suspects just yet.
Then Tei Sukone was taken in after the grocery store incident. Thinking logically, Detective Shion took a swatch of Tei's hair and sent it to the crime investigation lab. Akiko then compared Tei's hair to the hair found on the previous crime scenes, and announced it the same. Ia took the fingerprints from the corpse and compared them to Tei's. They were also a match.
Haku Yowane and Aoki Lapis had their lives turned upside down and one taken after Tei had discovered they both were allies with Miku Hatsune and became enraged at them.
Tei Sukone was found guilty of two counts of first degree murder, one count of robbery, and one count of kidnapping a minor and was sentenced to death.
Detectives Kagamine, Shion, and Yuzuki, Ia and Akiko, Doctors Merli and Cul, and Officers Sakine, Kamui, and Kagamine were given the credit of solving the case that if not for their excellent research might have gone cold.