Yes, there is proof in the Book and the Sunnah that jinn enter humans. In the Qur'aan, Allaah Almighty Says:
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Those who eat Riba (usury and interest) will not stand (on the Day of Resurrection) except like the standing of a person beaten by Shaytaan leading him to insanity [Al-Baqarah 2:275]
Ibn Kathir, may Allaah have mercy upon him, commented: "They will rise from their graves like a person rises who is possessed by the Shaytaan."
Regarding proof from the Sunnah, the Messenger of Allaah Salallaahu alayhi wasallam said, "Indeed, Shaytaan flows through the son of Adam like the flow of his blood." (Al-Bukhaari no.2039 and Muslim no.2175)
In Manqalat Ahl As-Sunnah wal-Jamma'ah, Al-Ash'ari said that they -meaning Ahl As-Sunnah- say that the jinn enter into the body of the possessed as proven by the preceding verse.
'Abdullaah, Imaam Ahmad's son, said, "I said to my father that a group of people claimed that jinn don't enter into the bodies of human beings. He said, 'O my son, they are lying; don't you see that it is they who are speaking upon their tongues."
In a number of Hadiths from the Messenger of Allaah Salallaahu alayhi wasallaam, recorded by Imaam Ahmad and Al-Bayhaqi, it is reported that he met a boy who was possessed. So the Prophet Salallaahu alayhi wasallaam began saying, "Come out, O enemy of Allaah. Come out, O enemy of Allaah." (Ibn Majah no.3548)
In some versions he said, Come out, O enemy of Allaah. Come out, O enemy of Allaah." (Ahmad 4/171, 172)
Then the boy healed and became normal.
Here we have mentioned one proof from the Qur'aan and two from the Sunnah; what people witness everyday serves as tangible evidence, not to mention that this is the view of Ahl As-Sunnah wal-Jama'ah. Nevertheless, we do not deny that some people are insane due to some other defect in their mind.