They say 49-year-old Mark Alan Andrews is in San Luis Obispo County Jail and has been charged with homicide.
Officials say he lives in the same neighborhood as the victim, Colleen Maria Barga-Milbury.
A search warrant was served at Andrew’s home. According to reports, police found a rifle consistent with the firearm they think was used to murder Barga-Millbury.
They also found a live hand grenade. The San Luis Obispo Sheriff's Department Bomb Squad was called in to take care of it.
Officials found several other firearms at Andrew’s home.
Detectives say there is no evidence to suggest the victim had any conflict with Andrew’s prior to the homicide. They are searching for a motive and determining if Andrew’s mental health issues played a role in the homicide.