" Crack investigative methods" would be very intelligent or smart ways of investigating a crime.

“Crack investigative methods”将是非常聪明或巧妙的犯罪调查方式。

In detective stories, the hero of the story is a detective or a police officer who investigates a crime- usually about someone who has been killed.

在侦探故事中，故事的主人公是调查犯罪的侦探或警察——通常是关于被杀的人。