Who killed Laura Palmer
23 episodes of Twin Peaks carry this thread, 1d 0h in all — 20 of them are in The Essentials.
Arc membership is derived from each episode's own title and summary text. It shows where a thread is foregrounded, not every episode it touches.
In airing order

The small northwest town of Twin Peaks, Washington is shaken up when the body of the Homecoming Queen, Laura Palmer, is discovered washed up on a riverbank, wrapped in plastic.

Agent Cooper enjoys the comforts of the Great Northern Hotel. Bobby Briggs and Mike Nelson are released from jail. Doctor Hayward hands over the autopsy report on Laura Palmer.

Ben Horne's brother, Jerry, arrives in Twin Peaks; together they travel to One Eyed Jack's and meet with the madam, Blackie O'Reilly. Audrey leaves a clue for Cooper. Deputy Hawk finds a bloody towel near the crime scene.

Cooper meets with Audrey, who confesses to leaving him the note about One Eyed Jack's. Cooper tells Truman he can't remember who the killer was in his dream, but insists the dream is a code to solving the crime.

Cooper questions Dr. Jacoby, who suspects Leo Johnson is the killer. Gordon Cole, Cooper's supervisor, calls in with Albert's report. Josie Packard spies on Ben Horne and Catherine Martell. Hawk tracks down the One-Armed Man.

Cooper and company have tea with the Log Lady, who tells them there was a third man following after Leo and Jacques the night Laura died. At Jacques Renault's cabin Cooper, Hawk, and Truman find Waldo the bird

Audrey cons her way into working at the perfume counter where Laura worked and discovers that it's being used as a recruitment post for One Eyed Jack's. James, Donna and Maddy plan to lure Jacoby away from his office

Audrey is hired at One Eyed Jack's, but is caught in a trap when her father arrives. Cooper gets Jacques Renault to reveal the details of Laura's last night in the cabin. Deputy Andy saves Truman's life and apprehends Renault

A wounded Agent Cooper has a vision of a giant who gives him several clues about the murder of Laura Palmer. Shelly and Pete recover from the mill fire, but Josie and Catherine are missing

Albert determines that neither Leo nor Jacques killed Laura, but he is unable to find any leads into who shot Cooper. Cooper says they must find the third man, who he believes to be Bob, the gray-haired man.

Ronette is attacked in her hospital bed by an unseen person. Jean Renault, brother of Jacques and Bernard, plans to blackmail Ben Horne for the release of Audrey. Donna meets with Harold Smith, a shut-in who had befriended Laura

Leland confesses to killing Jacques Renault. Andy wants to take a new sperm count test. Rumor spreads that a food critic is coming to Twin Peaks. Jean asks Ben to set a trap for Cooper in exchange for Audrey's life.

Cooper remembers the message under his bed. Shelly and Bobby begin Leo's home care. Sternwood hears pretrial motions and declares Leo not fit for trial. Nadine comes home, still thinking she's in high school

James saves the girls from a tormented Harold. Cooper brings Audrey home. Bobby and Shelly learn that their insurance plans have backfired. Donna tries to convince Truman that Harold Smith has Laura's secret diary

Cooper and the One-Armed Man inspect guests at the Great Northern. Hawk finds Harold Smith dead - with a mysterious suicide note and the diary torn to shreds. Leo speaks to Bobby about "new shoes.

Donna and James wonder why Maddy left so suddenly. Norma's mother arrives with the news that she's married a new man, Ernie Niles. Cooper tells Leland they arrested Ben Horne for Laura's murder.

Albert returns to examine Maddy. Cooper asks for twenty-four hours to finish his case. James and Donna reaffirm their love. Andy accidentally leads Donna and Cooper back to Mrs. Tremond's house

Leland is laid to rest and Sarah Palmer tries to accept all that has happened to her family. Dr. Jacoby returns from Hawaii. Cooper prepares to leave Twin Peaks. Mayor Milford objects to his brother's engagement to a younger woman.

Ben takes Bobby under his wing in a hope to destroy Hank and Jean. However, Ben's mental state is starting to crack. Cooper starts to look at buying real estate. Major Briggs's supervisor reveals that Briggs was studying the woods.

Windom Earle has taken his first victim in the deadly chess game. Audrey tells Bobby they have to save Ben from his civil war fantasy. Leo awakes and attacks Shelly, but Bobby is able to fend him off.

The police look for James in the Marsh murder. Bobby and Shelly tell Truman that Leo escaped; and Bobby reveals that he saw Hank shoot Leo the night the mill burned. Albert returns to Twin Peaks with information on Windom Earle.

Bobby and Shelly reaffirm their love. Cooper calls Shelly, Donna and Audrey together to warn them about Earle. Briggs shows Cooper a tape of Windom Earle making a report on his quest for the Black Lodge.

Laura is the one.