Some very basic ideas to help you plot a mystery.

PROVIDE COMPELLING CHARACTERS:

1. Every character has at least one secret, although the reader may never learn about it if it doesn’t add to the plot as you go. Set these secrets up before you begin, or, if you’re a non-plotter, you should come up with these secrets as the character appears and before you’ve written much about him or her.
2. Most every character is reluctant to talk to the detective for a good reason.
3. Every character tells at least one lie when talking to the detective.
4. The detective suspects everyone he talks to, finds out if person had motive, opportunity and means. In one out of two interviews or more, he finds a clue and/or red herring–may not know it’s a clue when he notices it. Scatter them around. Use senses–see, hear, smell, taste, touch.
5. Most every character the detective talks to has a reasonable motive for murdering the victim.
6. Most every character had the opportunity to murder the victim.
7. Most every character had the means to murder the victim.
8. Several characters implicate another character, either overtly or subvertly. They give possible motive, opportunity, and/or means for other characters.

PROVIDE CONFLICT AND TENSION:

1. When the detective asks in interviews about opportunity and means, she upsets suspect.
2. When the  detective finds an interviewee in a compromising position.
3. When bad guy begins to stalk detective.
4. When police become annoyed at detective for interfering.

DETAILS:

1. At least one unique location.
2. One character at least with a unique/interesting occupation or hobby.
3. One character who is quirky or funny or eccentric.

All the above is a start. But I believe if you use most or all of these ideas, your story will be richer and better for it.