"So you're quite shook up about this then?" asked the detective.

"And what did you think of that?" inquired the detective.

"Where were you when they died?" questioned the detective.

Okay, I need help with the dialogue.
Is it correct the way it is thanks.
If not, how would I change it.

it looks correct to me

All of those are quite appropriate. However when writing dialogue, it is not always necessary to say "asked the detective." If there are only two speakers , you can just indent each time the speaker changes. If you wish to change the mood of the person talking you can use verbs like "interrupted", "menaced", "soothed", etc.

Check this site.

http://mrbraiman.home.att.net/page13.html

The dialogue you provided is grammatically correct. However, if you would like some suggestions on how to vary the language or structure of the dialogue to add more depth or realism, here are some possible changes:

1. "So you seem quite shaken about this, huh?" asked the detective.
Note: "shook up" can be substituted with "shaken" for a more formal tone.

2. "And what are your thoughts on that?" inquired the detective.
Note: "did you think" can be replaced with "are your thoughts on" to inquire about the person's present opinion.

3. "Do you mind telling me where you were when they died?" questioned the detective.
Note: "were you" can be changed to "you were" for a smoother sentence structure.

Remember to consider the characters, their personalities, and the context in which the dialogue takes place while making any changes.