The game opens with a call for an evidence search near Santa Fe St. Head for the mission marker and you'll automatically leave the car.
Head down the alley near the stairs and you'll find a couple of crappy items on top of the stacked up boxes.
Approach the newspaper and examine it. Tilt the analog stick around to make Cole focus on a certain part of the paper. Vibration is the strongest indication that you're looking at the right place.
After the cutscene your partner will call your attention to the back alley. Follow him and examine the blood stains on the wall.
Now turn left from the door and walk a little forward. Cole will find the gun at the rooftop. Head over to the end of the alley and turn left afterwards.
You'll find a yellow pipe near the end of the third alley, use it to climb up to the rooftop then turn left and approach the murder weapon that's on the ground.
Examine the revolver and tilt your analog stick around to get Cole to focus on the make and model of the gun. After acquiring the serial number, inspect the weapon further to find that 2 bullets have been fired from it.
After acquiring everything you need from the gun, head back down and walk back to your car. Cole will automatically open his notebook, click on the gun store and place it as your next destination. Now drive all the way to Central Avenue.
Once there the gun shop owner will be kind enough to show you his ledger of people who have purchased guns. Look through the book and find the man called Errol Shroeder who purchased a gun with nickel plating and pearl grip.
Leave the gun shop and enter your car, then mark Shroeder's apartment as your next destination and drive to South Gless Street.
Enter the apartment building and examine the mail box immediately at the right side of the door as soon as you enter. Once you have his room number head up the stairs and knock on the door that corresponds to Shroeder's name.
Shroeder will greet you at the door and attempt to fight back as soon as you try to capture him. Brawil him and knock him out to contain him.
Once he's cuffed and secure you'll need to look around the apartment. Head over to the drawer that Shroeder opened earlier and pick up the green notebook inside.
Open the notebook and flip over to the next page to find a name that Cole will find interest in. Your partner will then call your attention and ask you to stop investigating, ending the mission.