Holding the mushaf (copy of the Qur’an) in your hands is permissible during the performance of the Tarawih.

Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states the following: There is nothing wrong with reading from the Qur’an by holding the mushaf (copy of the Qur’an) in your hands. We have precedents for this in the practice of as-salaf as-salih or the pious forbears; we read in the sources that `A’ishah, the beloved wife of the Prophet (peace and blessings be upon him), told her mawla (client) to lead them (women) in Tarawih, while doing so he was reading from the mushaf (as per her instructions).

Based on this, there is nothing wrong as a prayerful Muslim, in reading from the mushaf while performing Tarawih.