It's a Mad, Mad, Mad, Mad World

"Smiler" Grogan (Jimmy Durante), an ex-convict wanted by police in a tuna factory robbery fifteen years ago and currently on the run, careens his 1957 Ford Fairlane off twisting, mountainous State Highway 74 near Palm Springs in Southern California and crashes. Five motorists stop to help him: Melville Crump (Sid Caesar), a dentist; Lennie Pike (Jonathan Winters), a furniture mover; Dingy Bell (Mickey Rooney) and Benjy Benjamin (Buddy Hackett), two friends on their way to Las Vegas; and J. Russell Finch (Milton Berle), an entrepreneur who owns Pacific Edible Seaweed Company in Fresno. Just before he dies (literally kicking a bucket), Grogan tells the five men about $350,000 buried in Santa Rosita State Park near the Mexican border under "The Big W".
Initially, the motorists try to reason with each other and share the money, but it soon becomes an all out race to get the money first. Unbeknownst to them all, Captain T.G. Culpeper (Spencer Tracy), Chief of Detectives of the Santa Rosita Police Department, has been patiently working on the Smiler Grogan case for years, hoping to someday solve it and retire. When he learns of the fatal crash, he suspects that Grogan may have tipped off the passersby, so he has them tracked by various police units. His suspicions are confirmed by their behavior. Everyone experiences multiple setbacks on their way to the money. Crump and his wife Monica (Edie Adams) charter an old WWI-era Jenny biplane and eventually make it to Santa Rosita, but are soon unknowingly locked in the basement of a hardware store by its owner (Edward Everett Horton). They eventually free themselves with dynamite. Bell and Benjamin charter a modern plane, but when their wealthy alcoholic pilot (Jim Backus) knocks himself out drunk, the two are forced to fly and land the plane themselves. Finch, his wife Emmeline (Dorothy Provine), and his loud and obnoxious mother-in-law, Mrs. Marcus (Ethel Merman), are involved in a car accident with Pike's 1954 Ford furniture van. The three flag down British Army Officer Lt. Col. J. Algernon Hawthorne (Terry-Thomas) in his 1951 Willys station wagon and convince him to drive them to Santa Rosita. After many arguments, most caused by Mrs. Marcus, she and Emmeline refuse to go any farther, and Finch and Hawthorne leave them by the side of the road in Yucca Valley.
Pike tries to get motorist Otto Meyer (Phil Silvers) in his ivory-colored 1948 Ford convertible to take him to Santa Rosita, but he is betrayed, and the greedy Meyer races for the money on his own, leaving Pike stranded with only a little girl's bike from his furniture van. A furious Pike later meets up with Meyer, bent on retribution. Enraged by Meyer, Pike literally destroys a gas station owned by two brothers, Ray and Irwin (Arnold Stang and Marvin Kaplan), single-handedly.
Pike steals Ray and Irwin's Dodge M37 tow truck and meets up with Mrs. Marcus and Emmeline and picks them up. While in a town called Plaster City, Mrs. Marcus calls her devoted, powerfully built, but dim-witted son Sylvester (Dick Shawn), who lives on Silver Strand Beach near Santa Rosita, to get the money for them, but misunderstanding and believing his mother is in trouble, he instead races to her in his red 1962 Dodge Dart convertible. Meyer experiences his own setbacks, including sinking his car while trying to cross the Kern River and nearly drowns. He manages to steal a blue 1956 Ford Sunliner belonging to a passing motorist (Don Knotts) by telling him he's with the CIA and re-joins the hunt. All the while, Culpeper and the police department observe their activities from afar. Around this time, two taxi drivers (Peter Falk and Eddie "Rochester" Anderson) get in on the chase in their 1959 Plymouth Yellow Cabs.
Eventually all the characters arrive at Santa Rosita State Park at the same time and search for the big W. Emmeline, who wants no part of the money, looks up from taking a drink from a water fountain and sees, in the distance, "The Big W", composed of four palm trees growing in the shape of the letter "W". Pike finds it next and informs everyone else. Culpeper, who saw Emmeline's discovery, orders all policemen to leave the area, and goes in solo to retrieve the money. However, after suffering a gradual but extensive personal breakdown during the course of the day, he now plans to take the money to Mexico to escape a dysfunctional family and an apparently unappreciated career with a very small pension. After everyone digs up the money, Culpeper identifies himself and talks them into turning themselves in, promising a jury will be more lenient. But when the group sees Culpeper fleeing with the money, they realize what's happening and give chase in the two 1959 Plymouth cabs. At that point, Chief Aloysius (William Demarest), who had blackmailed (unbeknownst to Culpeper) the mayor to triple Culpeper's pension, reluctantly tears up the pension papers and orders Culpeper's arrest.
After a long chase sequence, all of the men end up stranded on the fire escape of a condemned office building. The suitcase of money opens, and the money falls into the streets below, where passers-by scoop it up. The men all try to climb down a fire truck's extension ladder even though the fireman (Sterling Holloway) told them "one at a time". Their combined weight causes the firemen to lose control of the ladder, causing the ladder to fling them into various locations, causing many injuries and landing all of the men in the prison hospital wing. The group, in various stages of traction, criticizes Culpeper for taking the money, but he rebukes them, saying they will likely get off easily despite their recklessness because he will have the harshest sentence. He wonders if anything will ever make him laugh again, given that his wife is divorcing him, his mother in-law is suing for damages, his daughter is getting her name legally changed, and he is losing his pension. At that moment Mrs. Marcus, flanked by Monica and Emmeline, enters, begins to berate everyone, and promptly slips on a banana peel carelessly tossed by one of the men before the women entered the room, and is carried out on a stretcher, still berating everyone, including those carrying her out. All the men, except Sylvester, begin to laugh hysterically despite the pain it causes; within seconds even Culpeper joins in.

Question: What case has Culpeper been working on for years?
Answer: Smiler Grogan