The Caprica City Police are a civilian law enforcement force in Caprica City, Caprica.
Sometime in her life, Socrata Thrace appears to have served in this police force as a patch is found in the scrapbook Thrace kept of her only daughter, Kara (Maelstrom).
Two police officers from this police force are briefly seen in the background on the Riverwalk before Caprica Six encounters Chantara and her baby (Miniseries).
Some time before the Fall of the Twelve Colonies, Laura Roslin is informed by two officers that her father and sisters died in a car accident (Daybreak, Part I). Unlike the officers seen on the Riverwalk, these officers wear "street cop" blues instead of dress uniforms.
It also seems that they have a SWAT team which can be seen briefly in Rebirth.
Closeup of the Caprica City Police patch.