You begin the mission on the rooftop of Police Headquarters. After the mission briefing, you can freely explore the rooftop to learn the basic controls. For the main task, you must sneak inside the police station through the air vent.
Approach the water tower by heading up the small ramp lined with coins. You will be introduced to special blue sparkles known as stealth auras, which line the ledge. These auras are used to pull off sneaky moves, such as sneaking along ledges. When close enough to the auras, press to interact, and then hold in the intended direction to sneak around the ledge. Use to jump across the two TV antennas to reach the air vent. Smash it with Sly's cane by pressing , then head inside until you reach a ledge above a vertical shaft of yellow lasers below. To reach the bottom, you must carefully leap down to the other ledges lining the shaft, avoiding the yellow lasers. If you hit a laser, the alarm will trigger, and they will turn red and deadly. Regardless if you trip the siren or not, you must destroy it to access the hallways.
As pointed out by Bentley, Carmelita's office is marked by the red door. Run through the corridor by turning left twice. The door is locked from the inside, therefore you must take an alternate route through the window on your right. There is another ledge you will need to sneak along to reach the window of Carmelita's office. Upon approaching the window, jump in and approach the vault. To switch between dials, you can use , or the directional left and right buttons. To turn the tumblers, you can either use , , or the directional up and down buttons.
Once done, the last thing you must do is escape to the van by heading down the fire escape and through the parking lot. Hop out onto the fire escape. Sly will then be confronted by Carmelita. While dodging Carmelita's shots, run down the fire escape lined with coins. Once at the bottom, make a run through the parking lot to reach the van. The lot is filled with a bunch of police cars and barriers. Do not jump over any of the police cars, as Carmelita will shoot them, causing them to burst into flames. Instead, run in between the vehicles and destroy any barriers that block your path.