Assalaamu alaykum. Is it allowed to read crime books for fun or to learn? Does it refer to Laghw or not?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

The general answer to the question is that if the books include violations of the Sharia, such as promoting corrupt beliefs, vices, and prohibitions or whatever negatively affects the Muslim's beliefs or ethics, then the principle is that it is impermissible to read them unless there is a need and the reader is equipped with religious knowledge and firm faith shielding him against their negative effects. Please refer to fatwa 86533.

As for the books that are free of Sharia violations, the basic principle is that it is permissible to read them.

In Islamic terminology, Laghw refers to any useless speech that serves no purpose, in which there is no good, and which does not amount to the level of sins. It also refers to all the prohibitions and misdeeds. Al-Qurtubi said:

"Laghw refers to all vain and pointless actions and statements. It includes singing and entertainment and the like. It also includes the foolish statements of the disbelievers, the harmful things that they say about the believers, immoral mention of women, and the like of evil speech. Mujaahid said, '{And they who turn away from Laghw} means that when they are harmed, they forgive.' It was also narrated that he said, 'When people talk about sexual intercourse, they refrain from participating in such conversation.' Al-Hasan said, 'Laghw refers to all sins.' This is a more comprehensive definition." 

Allah, The Exalted, urges the Muslims to give up Laghw and refrain from engaging in it. He says (what means): {Certainly will the believers have succeeded. They who are during their prayer humbly submissive. And they who turn away from Laghw (ill speech).} [Quran 23:1-3]

Laghw could also refer to the meaningless oath which has no legal effects; a person shall not be held accountable for such oaths. Allah, The Exalted, says (what means): {Allah will not impose blame upon you for what is meaningless in your oaths...} [Quran 5:89]

As the definition of Laghw in Islamic terminology becomes clear, the dear questioner can easily determine whether the books in reference fall into the category of Laghw or not; as we cannot give a general judgment on whether these books are considered Laghw or not.

Allah knows best.