Bell has completed his rehab, and he is once again handling cases on his own. He asks Watson to track down a witness who has decided she doesn't want to testify, and she handles it entirely without Holmes's participation. The witness is hiding out at the home of her old teacher, and she doesn't want to testify because she's pregnant and she's worried about getting shot to death by a murderous drug dealer.
In the main plot (you can tell it's the main plot because Sherlock Holmes is in it), a researcher named Barry Granger has been killed by having helium pumped into the bathroom where he's taking a shower. Then his body was staged to look like a suicide, but Gregson saw through that right away, so he called in the consulting detectives and told the rest of the police force to take the rest of the week off. There was a fake suicide note that referenced a mysterious letter-writer named "Adam Peer" who claimed that Granger faked his results. Granger was working on a breathalyzer that sensed cancer, and it was called "The Hound" as a way to sort of justify the strained pun in the episode title.
The investigation starts with Granger's boss, Hank Prince. His business was put in danger by the allegation that Granger's research wasn't genuine, and then it was put in danger when Granger died. And he's got an alibi: he was with his girlfriend, rather than the wife he's divorcing. So he's off the hook. Next, Holmes tracks down a woman that was seen arguing with Granger, and she turns out to be with the Mossad. Before she vanishes, she gives Holmes a thumb drive with all the emails that Adam Peer ever sent. There's a brief red herring, and then it turns out that Adam Peer was really two people. And one of them was Barry Granger!
So the Adam Peer that accused Granger of phony results wasn't really Adam Peer. The new theory is that Barry Granger was killed to damage Hank Prince. Then Hank's wife is found murdered with Prince's gun next to the body. Hank claims that he couldn't possibly have done it because he wouldn't leave his gun there. This convinces people for maybe five minutes, but then Holmes concludes that Hank's latest alibi is dependent on a taxi driver being easily distracted. So Hank killed Granger because he wanted to lower his stock price just long enough to keep his wife from getting a lot of money in the divorce, but then the price rebounded too early and he had to kill her.
When Bell goes to the house of the heroic teacher, he's decided that his witness doesn't need to testify. But the teacher is angry at what's become of his neighborhood, and he wants to take a stand. First, he offers to commit perjury to get the testimony into court. But when Bell rejects this, the teacher goes out and shoots the drug dealer to death and he gets shot dead in return. This bums Bell out and he doesn't want to go in to his "Welcome Back" party. Instead, he and Holmes go to a nearby coffee shop, which I think sounds like more fun anyway.
We open in the police station, where Bell has a paint can shaker on his desk. The idea is that it's part of some ribbing he's been receiving for finishing his rehab for his hand shaking. It's not the best joke, but I respect the guys on the force for actually going to a hardware store to buy the equipment. Bell wants Watson to help him with a case, in which a drug dealer named Quame Martenz shot and killed someone. I would have spelled it "Kwame," but I'm trusting the closed-captioning on this. Take it up with them. He had a great witness named Nicole Watkins, but she vanished and will no longer will be a witness, so Bell thinks she was threatened and he'd like Holmes and Watson to find her. Watson takes the case, of course. Also, there's a party being thrown to welcome Bell back to the ranks of Detectives without career-threatening hand tremors, and that's going to turn into a thing later in the episode. So watch for that.
In a lab somewhere, a man walks in and says hello to a mouse named Sherman. If I worked in a lab, I would have trouble not giving names to the animals, which would then make me very sad. I don't think I should work in a lab, is what I'm saying. Then goes to his desk and takes something out of a duffel bag before going to take a shower in the bathroom. There's a bathroom with a shower right next to his desk? I may have to rethink my position on working in a lab. As he takes his shower, go blurry and he staggers a little. He calls out, "Who's there?" in a strangely high-pitched voice. He sees a patch on the ceiling and rubber tubes coming under the door. In his squeaky voice, he says, "Please stop. I don't want to die." Then he lies down on the floor and dies.
The police are on the scene, along with Holmes and Watson. Gregson gives the lowdown. The dead man is Dr. Barry Granger. Although we last saw him dead in the shower, he's now at his desk with a bag over his head and tubes going from the bag to an air tank. And there's a suicide note, in which he says "It's all true." Watson says it's a reasonable suicide technique, since labs sometimes have helium, and it replaces the oxygen in your lungs. But, as Holmes notes, it's probably not suicide, because why would Holmes and Watson even be involved? Gregson says there are sweaty running clothes in the bag and the shower is wet. Holmes goes to the bathroom (I mean he walks to the room called "the bathroom," not that he just pees all over the crime scene) and spots something at the bottom of the door. There's residue of tape sealing the door up. Watson brings him some powder, and it reveals the shadows left by the rubber tubes. Holmes agrees that Granger was murdered by helium being pumped through three hoses under the doorway: "He was dried, clothed, and staged."