To investigate a murder means to carefully examine and gather information about a killing to understand how it happened, who is responsible, and why it occurred. Full definition
X While investigating the murder of a beautiful woman, a detective falls in love with her memory, only to discover she may not really be dead! (kqek.com)
An African American police detective is asked to investigate a murder in a racially hostile southern town. (metacritic.com)
You begin investigating a murder, and before long you'll be trying to save the world. (controlcommandescape.com)