CCC# 1013 Death is the end of man's earthly pilgrimage, of the time of grace and mercy which God offers him so as to work out his earthly life in keeping with the divine plan, and to decide his ultimate destiny. When "the single course of our earthly life" is completed, we shall not return to other earthly lives: "It is appointed for men to die once." There is no "reincarnation" after death.
It states clearly There is no reincarnation after death. The belief in reincarnation, also called metempsychosis (which is Greek for animate afterward ) of course believes that souls inhabit a series of bodies and can live many lives on this earth before being completely purified, and so released from the need to migrate to another body. According to this belief the soul pre-exists its embodiment and after death exists in a disembodied state before animating once again a body of the same or different species. In various forms, reincarnation has been accepted by Buddhists, Hindus, Neoplatonists, and others. But belief in the resurrection and official rejection of the preexistence of souls rule out reincarnation by Catholics, or Christians, for that matter. By maintaining an indefinite series of chances, the doctrine of reincarnation reduces the seriousness of God’s grace and of human liberty, exercised in one life that is terminated by a once-and-for-all death. So in summary, the Catholic Church has never nor will it have a belief in reincarnation because it is in total opposition to the central beliefs of the faith.