"Well you picked the right place Cole: a city that needed an honest cop like a thirsty man needed water. You heard the stories, but you weren't interested. You were here to fight the good fight, solve cases, right wrongs; but the force is like politics. There's no sitting on the fence. You have to choose sides. A brown paper envelope, or a Greyhound ticket to Palookaville. It can only ever end one way."
Since this is an early case in the game, you can be aggressive with little harmful effect. Leave cover as soon as possible, shoot any crooks outside and shoot through the glass at crooks inside. If you kill at least three, your partner can take out the rest, so just lay back. Keep in mind that a shotgun is a close range weapon, so try to get as close as you can without becoming a target for the criminals, normally there are 5 armed robbers in total in this case. There will be at least one armed with 12 Gauge Pump Action Shotgun, and one robber will hold Thompson M1. However, you cannot obtain them.
You can finish this case without your shotgun and use your service revolver, the Colt Police Positive instead; however, your partner will still make shotgun-related comments.
In the introduction before the case, Herschel Biggs narrarates and uses the phrase "a one-way ticket to Palookaville", a phrase that was first coined in the 1954 film On the Waterfront. L.A. Noire takes place in 1947, before the film came out. This was likely a developer oversight.