Hello DeeJay, and welcome to the Forum!
Some of the first documented cases of non-Christian cases were reported by a Christian by the name of Dr. Ian Stevenson. You can find some of these in his book, "20 Cases Suggestive of Reincarnation". The bulk of cases investigated by him and his successor, Dr. Jim Tucker, happens to involve non-Christians.
Until reports of the Bridey Murphy story in the 50's, most people believed that cases of Reincarnation only seemed to exist among non-Christians. However, with the introduction of Yoga, Transcendental Meditation and Hypnotic Therapy in the West we have seen a growth in awareness of Reincarnation among Christians during the last 50 years.
Today, it would seem to English-speaking readers that the best Reincarnation cases only seem to involve English-speaking Christians. However, these constitute only the tip of the iceberg, since most known cases involve non-Christians.