Steve Martin had just one edit. He was completely game to sing this absurd, tongue-twisting, joke-packed patter song about three infants who are all suspects in the murder of their mother — but he hesitated on the line: “Should a baby get fried for matricide?”

“Guys,” he said from the recording booth, “I don’t know that we should be talking about sending babies to the electric chair. Maybe we could just do ‘Should a baby get tried for matricide?’”

The “guys” were the award-winning Benj Pasek and Justin Paul, who co-wrote the song “Which of the Pickwick Triplets Did It?” for the third season of “Only Murders in the Building.”

“We were like, ‘Wait, not only did you solve something with an exact perfect rhyme, but it means we don’t have to electrocute babies and we can make it into a murder trial?’” Pasek says. “‘This is why you’re Steve Martin.’”

Pasek and Paul didn’t know it, but among his many other talents — comedian, actor, banjo player — it turns out that Martin is a huge fan of “The Music Man.” At one of Martin Short’s legendary Hollywood Christmas parties some years ago, Martin did that show’s rapid-fire patter song “(Ya Got) Trouble” and did it “word perfect,” says Marc Shaiman, the multi-Oscar- and Emmy-nominated composer, who was there. “So we kind of knew: Oh yeah, he’s gonna nail this.”

The latest season of the murder mystery comedy series gave Short’s character, Oliver Putnam, a chance to turn his murder mystery stage play into an outrageous Broadway musical called “Death Rattle Dazzle!” Martin’s character, veteran TV actor Charles-Haden Savage, plays a constable investigating the murder of the triplets’ mother — and one story thread in the season is whether he can get through the intricate song without going into a wild fugue state onstage.

“And the harder that it was to actually perform,” says Paul, “and the more alliterative or the more plosives that there were, the more twists and turns or the pace of the song, the more of a payoff for you as an audience. You’re wondering: ‘Can he actually do it?’”

Showrunner John Hoffman brought Pasek and Paul, the songwriting team behind “Dear Evan Hansen” and “La La Land,” into the “Only Murders” writers’ room to create this faux musical. They wrote a lullaby for Meryl Streep’s character and several other theatrical numbers, working with handpicked collaborators including Sara Bareilles and Michael R. Jackson.

For the “Pickwick” patter song, they reached out to Shaiman and Scott Wittman, the theater veterans who musicalized “Hairspray” and “Charlie and the Chocolate Factory” — and who actually gave Pasek and Paul their big break on Season 2 of TV series “Smash” in 2013. This was their first time all working together, and it was like having “second-time-around marriages with younger people,” says Shaiman, 64. “They’re really like…”

“…trophy wives,” Wittman jumps in.

The two duos instantly hit it off and gathered in a room with laptops to play in the sandbox of a shared Google doc.

“Who would have ever known that four people writing lyrics could even work?” Shaiman says. “But it flows.”

“It was like we were playing a board game,” says Wittman, the goal being “how fast you could type to make the other person laugh.”

“The harder that it was to actually perform,” says Justin Paul, at right, … the more of a payoff for you as an audience.”

(Annie Noelker / For The Times)

It became a comedy writers’ room for songwriters, and they were all on the lookout for the best rhymes that matched words about babies with words about murder.

“Somebody would come up with ‘cradle / fatal,’” Paul says, “and then Scott would jump in and shout, ‘NEONATAL!’”

“And we would all just howl,” Pasek says.

When Charles first attempts the manic word salad, it sends him into the “white room” — a panicked void where stage performers go when they forget their lines. He discovers that making omelets, his soothing practice, helps him get through the song — but it’s an untenable crutch. Oliver brings in Matthew Broderick, playing himself with exaggerated smarm, who effortlessly breezes through the patter song.

“What can I say?” Broderick says. “I’m a vessel.”

Finally, during the sitzprobe (orchestra rehearsal) for the musical, Charles has to perform the entire song for an extra reason — to create a distraction and help his sleuthing partners, Oliver and Mabel (Selena Gomez), in their investigation into the murder of Paul Rudd’s character. So it’s a true nail-biter to see if he can get through this incredibly dense and complex tightrope that has been tripping him up all season long.

It was like that on set too.

“Everyone had wrapped, and everyone stayed,” says Wittman, who was in the Washington Heights theater where the scene was being shot. “The day had gotten away from them and they only had two hours to film the actual number.

“But Steve — not one bead of sweat. He nailed it every time. It was sort of thrilling.”