Refers to the official process of investigating crimes, typically by police or other law enforcement agencies.
The police began a criminal investigation into the murder case.
As a result of the criminal investigation, the suspect was arrested.
捜査 is a broader term for any investigation or search, while 刑事捜査 specifically refers to criminal investigations.
刑事 can mean 'detective' or 'criminal case', whereas 刑事捜査 is the investigative process itself.
Compound of 刑事 (criminal) and 捜査 (investigation).