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 is His slave and Messenger.
What you heard about being obliged to cover one's body with a sheet when sleeping is not correct. There is nothing in the Sharee’ah that stipulates this. However, a Muslim is required to recite what the Prophet used to recite before sleeping. In fact, this will protect him against all Jinn.
The Prophet said: “Whoever recites Aayatul-Kursy [i.e. verse 255, Chapter 2] in a night, Satan will not approach (come close to) him till the next morning.” [Al-Bukhari]
Besides, Ibn Mas’ood narrated that Prophet said: “Whoever recites the last two verses of Soorah Al-Baqarah [i.e. verses 285-286] in a night, they will suffice him.” [Al-Bukhari]
For more benefit about what to recite before sleeping, you may refer to the book Hisn Al-Muslim (fortification of a Muslim).
Allah knows best.