There is nothing wrong in reading from the mus-haf in supererogatory Prayer such as tahajjud and tarawih Prayers. The erudite Muslim scholar, Sheikh Nizam Ya`qubi, states: “This is a matter of disagreement among scholars. The Hanafi scholars do not permit this at all. The Shafi`i scholars permit it in both obligatory and supererogatory Prayers. The Maliki scholars hold a middle view, which I see more appropriate. They allow reading from the mus-haf in supererogatory Prayers, while they do not allow it in obligatory Prayers.
Having stated the above, one can read from the mus-haf in tahajjud Prayer, especially if this makes you recite more and helps you in memorizing more of the Qur’an.”