The "Elementary" episode "While You Were Sleeping" presents viewers with what appears to be a robbery but turns out to be very personal. The mystery and Sherlock's (Jonny Lee Miller) deductive skills are quite entertaining, although the mystery could have been solved more quickly if only Detective Bell (Jon Michael Hill) had believed in Sherlock's theory. At least he's got Captain Gregson (Aidan Quinn) to push things along a bit more quickly.
A man is shot in the head by someone who was sitting in a chair, and some of his things have been stolen. Holmes deduces that it was the neighbor who stole the dead man's things but that a woman wearing a specific type of deodorant did the killing. The neighbor saw the woman, but a sketch of her turns up a woman, Yvette Ellison (Amy Landon), in a coma. Of course, the cops assume the neighbor killed the man, because that fits their initial theory that it was a robbery gone bad.
Later, a black woman is shot in the same way. Sherlock sees that the woman resembles the man who had been killed, despite the difference in skin color. Tests show that the two were half brother and sister, but it turns out that neither of them knew the other existed.
Holmes deduces that the woman in the coma had a twin sister, Rebecca Ellison (Jennifer Ferrin), but they turn out to be fraternal twins. The coma sister (who the first victim's neighbor described) doesn't look much like Rebecca.
Sherlock learns that the murdered half brother and sister are both related to the Ellison sisters and that Rebecca was having them investigated. They are all related through the father. The father had told the Ellison sisters about the other two siblings on his deathbed, informing them that the "bastard" siblings may inherit tens of millions of dollars that they thought they were going to have to themselves.
Holmes gets Detective Bell to play along with a scene in Yvette's hospital room while Rebecca is present. Holmes pretends to fall apart, accusing Rebecca of faking her alibi. He also informs them that there is a third heir. He then shoves Bell. Bell arrests him and informs him he'll be spending the night in jail.
It is all a complicated trick to get the perpetrator to show herself by attempting to kill the fake third heir. It turns out that Yvette was using a doctor (with whom she's been having an affair) to fake her coma so she would have an airtight alibi!
An invasion of privacy
There was another sibling-like rivalry between Sherlock and Watson (Lucy Liu). Watson invades Sherlock's privacy by pulling out his old violin. He reacts by burning it to ash. He also retaliates by inviting an ex she has been dating over to his place for a nonexistent "party."
Watson is very upset at the idea of a two-way street when it comes to discussing private matters, as she feels Sherlock is the only one who should be sharing with his "sober companion." He's the one who needs the help, and it's her job to help him. He eventually gives in, pulling out another violin and playing it while Watson lies in bed, listening.