There has been scientific research on reincarnation and rebirth.
You can find information from the net. For example you can search
for 'Ian
Stevenson'. And many others who has likewise done research on
this subject...
http://www.buddhanet.net/e-learning/qanda05.htm
Exerpt:

Well, have there been any scientists who believe in rebirth?

Yes. Thomas Huxley, who was responsible for having science
introduced into the 19th century British school system and who was
the first scientist to defend Darwin's theories, believed that
reincarnation was a very plausible idea. In his famous book
'Evolution and Ethics and other Essays', he says:
In the doctrine of transmigration, whatever its origin, Brahmanical
and Buddhist speculation found, ready to hand, the means of
constructing a plausible vindication of the ways of the Cosmos to
man... Yet this plea of justification is not less plausible than
others; and none but very hasty thinkers will reject it on the
ground of inherent absurdity. Like the doctrine of evolution
itself, that of transmigration has its roots in the world of
reality; and it may claim such support as the great argument from
analogy is capable of supplying.
Then, Professor Gustaf Stromberg, the famous Swedish astronomer,
physicist and friend of Einstein also found the idea of rebirth
appealing. Opinions differ whether human souls can be reincarnated
on the earth or not. In 1936 a very interesting case was thoroughly
investigated and reported by the government authorities in India. A
girl (Shanti Devi from Delhi) could accurately describe her
previous life (at Muttra, five hundred miles from Delhi) which
ended about a year before her "second birth." She gave the name of
her husband and child and described her home and life history. The
investigating commission brought her to her former relatives, who
verified all her statements. Among the people of India
reincarnations are regarded as commonplace; the astonishing thing
for them in this case was the great number of facts the girl
remembered. This and similar cases can be regarded as additional
evidence for the theory of the indestructibility of memory.
Professor Julian Huxley, the distinguished British scientist who
was Director General of UNESCO believed that rebirth was quite in
harmony with scientific thinking. There is nothing against a
permanently surviving spirit-individuality being in some way given
off at death, as a definite wireless message is given off by a
sending apparatus working in a particular way. But it must be
remembered that the wireless message only becomes a message again
when it comes in contact with a new, material structure - the
receiver. So with our possible spirit-emanation. It... would never
think or feel unless again 'embodied' in some way. Our per
venalities are so based on body that it is really impossible to
think of survival which would be in any true sense personal without
a body of sorts... I can think of something being given off which
would bear the same relation to men and women as a wireless message
to the transmitting apparatus; but in that case 'the dead' would,
so far as one can see, be nothing but disturbances of different
patterns wandering through the universe until... they... came back
to actuality of consciousness by making contact with something
which could work as a receiving apparatus for mind. Even very
practical and down-to-earth people like the American industrialist
Henry Ford found the idea or rebirth acceptable. Ford was attracted
to the idea of rebirth because, unlike the theistic idea or the
materialistic idea, rebirth gives you a second chance to develop
yourself. Henry Ford says: I adopted the theory of Reincarnation
when I was twenty-six. Religion offered nothing to the point.. Even
work could not give me complete satisfaction. Work is fume if we
cannot utilize the experience we collect in one life in the next.
When I discovered Reincarnation it was as if I had found a
universal plan. I realized that there was a chance to work out my
ideas. Time was no longer limited. I was no longer a slave to the
hands of the clock... Genius is experience. Some seem to think that
it is a gift or talent, but it is the fruit of long experience in
many lives. Some are older souls than others, and so they know
more... The discovery of Reincarnation put my mind at ease... If
you preserve a record of this conversation, write it so that it
puts men's minds at ease. I would like to communicate to others the
calmness that the long view of life gives to us.
So the Buddhist teachings of rebirth does have some scientific
evidence to support it. It is logically consistent and it goes a
long way to answering questions that theistic and the materialistic
theories fail to do. But it is also very comforting. What can be
worse than a theory of life that gives you no second chance, no
opportunity to amend the mistakes you have made in this life and no
time to further develop the skills and abilities you have nurtured
in this life. But according to the Buddha, if you fail to attain
Nirvana in this life, you will have the opportunity to try again
next time. If you have made mistakes in this life, you will be able
to correct yourself in the next life. You will truly be able to
learn from your mistakes. Things you were unable to do or achieve
in this life may well become possible in the next life. What a
wonderful teaching!