The tour began just after dusk, as the lavender sky dissolved into night, backlit by the pulsing luminescence of Times Square.


Inside the Midtown South Precinct station house, a squat brick building on a relatively dark block of West 35th Street, a lieutenant poked his finger at a map tacked up on his office wall. He pointed out precinct jewels that his officers are tasked with safeguarding: the Empire State Building, the theater district, Pennsylvania Station, Grand Central Terminal and, “Oh, this other little spot called Madison Square Garden. Maybe you’ve heard of it?”


About 9 p.m., Officers Martin Reyes and Liza Hemme led a visitor to a police van parked outside. Officer Reyes got behind the wheel, while Officer Hemme slid open the side door and slammed it shut before jumping in the passenger’s seat. The police “peddler van,” named for the panhandlers and pickpockets frequently taken into custody, had a gamy stench, a cross between marijuana and body odor.


“Sometimes we arrest people who don’t smell so good,” Officer Reyes noted as he backed out of the parking space.


So began a journey into a parallel world, a backstage apart from Broadway’s gaudiness or gloss that most tourists never glimpse or even consider. There is no script here. No program that lists the night’s characters. It is a precinct as unpredictable as any, one in which officers once collared a costumed Elmo for patting a little girl’s buttock while posing for a photograph in Times Square. Or where Officers Reyes and Hemme once pulled over Harvey Keitel for a broken taillight, and Officer Reyes let the actor go with a warning and a compliment, “You were great in ‘Bad Lieutenant.’ ” Or where Officers Reyes and Hemme have spent chunks of time driving around tourists who cannot remember where they parked their car.


It is also where two officers posted outside the Empire State Building Aug. 24 fatally shot a gunman, Jeffrey T. Johnson, after he killed a former co-worker. Nine bystanders were wounded by police bullets, bullet fragments or ricochets.


On this breezy late-August night, the police van hiccupped and bounced over the streets’ grooves and potholes. The van’s turn signal was rhythmic and oddly loud, like the clippity-clop of a carriage horse.


“Disorderly group,” a dispatcher said over the police radio, the words interspersed with a never-ending buffet of crackles, croaks and beeps. The dispatcher relayed calls using police jargon and numbered codes, a language as foreign and hard to decipher as any spoken by the world’s tourists, swirling in herds outside the police van’s window.


“Disorderly group,” the chirp came again. “Riding bikes recklessly.”


Officer Hemme, a clipboard on her lap and a pen tucked between her fingers, grabbed the radio. “Ten-four.”


The nonviolent nature of the call did not merit lights and sirens, which can pose a danger in an area clogged with tourists and cars. En route to East 44th Street and Madison Avenue, the location of the complaint, Officer Hemme helped navigate the boxy van through traffic. “Watch out. There’s a nice fat Rolls-Royce over here,” she said.


They have been partners for 10 years, six of which were spent shoulder-to-shoulder on foot patrol. Officer Reyes always drives because his partner had back surgery, he said.


“What if we get into an accident and her pins pop out?” he said, glancing at her paternally from the corner of his eyes.


“You had a cataract; so I don’t know what you’re talking about,” she said. “You know what they say about old age: it doesn’t come alone.”


Officers Reyes, 47, and Hemme, 42, seemed like the law enforcement equivalent of a long-married couple. They know each other to a comforting fault.


Officer Hemme knows, for instance, that her partner is allergic to “nuts, legumes, pineapples, apples, apricots ...” The list went on. She learned of his allergies the hard way, she said. When they first partnered, she gave him an almond pastry and “his lips grew so swollen, they almost split open.” The reaction was so severe that a superior wanted her to take him to a hospital. Another time, she bought him a pineapple smoothie and he broke out in welts.


“I always joke that I know how to kill him,” she said.


Officer Reyes knows that his partner does not like to wear her hair long, which is fine by him because the hairstyle makes her grouchy, he said.


Officer Reyes, a married father of a grown son, is short and stocky with a doughy face, which spouts a dimple when he smiles. The son of Mexican immigrants, he was raised on a Colorado farm, where his family grew barley for Coors beer and potatoes for McDonald’s fries. He has a Southwestern accent and is prone to precede a stray thought with, “I’ll tell ya what ...” He will point lost tourists in the right direction and bid them goodbye with a wink, his version of a handshake.


Officer Hemme was born in the Bronx, near Yankee Stadium, though she grew up mostly in the Whitestone section of Queens. She is tall; her fair and lightly freckled face is framed by a short, sandy blond bob and funky eyeglasses with olive-colored frames that match her eyes. She is fast-talking and wickedly funny. When asked about her police shield — No. 665 — she threw her shoulders back, hands on hips, and said, “One short of the devil.”