This week's murder is a grisly one, as a ballerina is found cut in two during a dance rehearsal. In spite of the gory spectacle of her halving, Watson quickly concludes that the actual cause of death was a slit throat the night before--Detective Bell is on hand to investigate with them, having finally escaped desk duty.
Dance with Death
The first suspect they interview is the company's lead dancer, a woman named Iris who Sherlock
is familiar with and a great fan of. While Watson thinks she might have had motive to kill a rival ballerina, Sherlock is quick to dismiss the possibility that they could possibly be anywhere near the same level, analogizing that it would be as pointless as him trying to kill the world's second best detective. All the same, her supposedly missing box cutter is determined to be the murder weapon, and she's arrested when her alibi falls through. Sherlock quickly manages to exonerate Iris by sleeping with her, judging her to have sustained a dance injury that would have rendered her incapable of cutting the victim in half.
Sherlock's next suspect is a creepy paparazzo who had been following Iris, the suspicion being that he wanted to frame her after she smashed his camera. At the same time, the NYPD discovers a voicemail that reveals a romantic relationship between Iris and the victim--her phone had been bugged by the paparazzo, and the voicemail had somehow been leaked to the press. Sherlock believes that the killer was the one who leaked the voicemail.
Helping the Homeless
Watson, meanwhile, is pursuing a strange charity case: a homeless man's friend Zeke Frebo has gone missing, and for some reason Joan is determined to find him. She tracks down Frebo's sister, and learns that he had been on the streets since returning from Afghanistan, as he'd fallen victim to PTSD and drugs. She later explains to Sherlock that her biological father had been homeless and schizophrenic, which is why she volunteers her services for that community.
Watson links the missing man's brand of cigarettes back to his sister's house, suggesting that he's staying there -- it turns out that she wasn't his sister at all, and had been keeping him locked up in her house along with two other homeless people, collecting their government benefits.
Sherlock cracks his own case open by tracing the ambient noise on the voicemail to her lawyer's office; he confronts the lawyer about his suspicions, outlining how the lawyer was trying to star in a sensational court case, but he denies everything -- he has Iris laying low somewhere with a new cell phone number, and intends to turn her against Sherlock before he can get to her. Luckily, Sherlock is able to get a search warrant to investigate his home, where the police force finds a hard drive with security footage of the murder.
One of the strange things bout this episode is how isolated the two plotlines are from each other; while Joan's initiative to help the homeless provides interesting backstory, it has almost nothing to do with Sherlock's ballet antics--all the same, it's nice to see Watson solving one by herself.