You say "Did you read that book?" when you talk about a specific time (in the past) you have in mind. For example - last week or yesterday. When you want to ask if they have EVER (in their life) read the book you say "Have you read that book?" :)

Both are good: - Did you read that book; you know, the one I lent you last month? (I imagine that you will I have read it already...) - Have you read that book that I lent you last week. (I am not sure whether you will have read it because I only lend it to you recently).

Have you read that book?

Both are correct.

Have you read that book? sounds correct .