The opening of Laura establishes the contrasts between Lydecker and McPherson. Lydecker, by virtue of his intellect, position and possessions, firmly believes he is above everyone including one more detective. His home reflects his character. McPherson presents himself passively but strongly - you get the impression that he can handle himself in any situation, with anyone. This sets up the conflict you know is coming.
There is no build-up to the murder - the opening line tells us that. What follows is the necessary dark uncovering of the lives involved with and impacted by the murder.