Here are some words for your vocabulary

• alibi - an excuse that an accused person uses to show that he/she was somewhere else than at the scene of the crime
• breakthrough - an advance or discovery that helps solve a crime
• clue - a fact or object that helps to solve mysteries
• crime - an act committed in violation of the law
• deduce- to infer by logical reasoning
• detective - a person who investigates crimes and gathers information
• evidence - something, such as a witness statement or object that is used as proof in a crime
• hunch - a guess or feeling not based on known facts
• motive - an inner drive that causes a person to do something or act in a certain way
• mystery - something that is secret and unknown
• purloin - to steal or filch
• red herring - something that is used to divert attention from the basic issue
• sleuth - another name for a detective
• suspect - a person who is suspected of a crime
• victim - someone who is harmed or suffers some loss
• witness - someone who saw or can give a firsthand account of something