Homicide Case #6 - The Quarter Moon Murders - L.A. Noire wiki

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Central Police Station:

Examine the letters for the Black Dahlia Letter and Shelly Exerpt.

Pershing Square:

Climb the water fountain to find Second Shelly Exerpt and Social Security Card.

The description of the Hall of Records on the main map matches the Second Shelly Exerpt.

Hall of Records:

Scale the Chandelier.  To get there you can see one of the support cables runs to a platform.  Around the corner is a door to a room with a ladder that accesses that platform.

On the Chandelier you will find Deidre Moller's Missing Watch and the Third Shelly Exerpt.

The description of the L.A. Public Library on the main map matches the Third Shelly Exerpt.

L.A. Public Library:

Climb to the top.

At the top in the corner opposite the ladder, there is Antonia's Medallion and the Fourth Shelly Exerpt.

The description of the Westlake Tarpits Library on the main map matches the Fourth Shelly Exerpt.

Westlake Tarpits:

Reach the Island by following the sunken docks.

On the island you will find one of Theresa Taraldsen's Shoes and the Fifth Shelly Exerpt.

The description of the L.A. County Art Museum on the main map matches the Fifth Shelly Exerpt.

L.A. County Art Museum:

Reach the center of the maze.  From the start of the maze: right at the first branch, right at the 4-way and immediately left, go straight at the next branch and that's it.  Luckily you don't have to find your way out.

On the sculpture you will find Celine Henry's Ring and the Sixth Shelly Exerpt.

The description of the Intolerance Set on the main map matches the Sixth Shelly Exerpt.

Intolerance Set:

Climb to the Throne.  Go straight under the pillar through the gates to the stairs.  Balance on the pillar, after you jump off use the ladder to your left to get to the throne.

On the throne you will find Evelyn Summers' Ring and the Seventh Shelly Exerpt.

Escape the set.

The description of the Christ Crown of Thornes on the main map matches the Seventh Shelly Exerpt.

Christ Crown of Thornes:

After confronting Garrett Mason, Run outside to the other building, there is a door to the left that leads to the catacombs.