Sofrim, Chapter 3:
A Torah scroll may never be cut into separate books but is only valid in it’s entirety.
When a Jew hands a Torah scroll to another Jew, he should do so with his right hand. The Jew receiving the Torah scroll should do so with his right hand. The Gemara here states that the Torah was delivered at Mount Sinai in this matter.
Kabbalistic literature actually teaches that the right side means Chesed (Kindness) whereas the left side stands for judgment (Gevurah). G – d created this world with Chesed and He apparently gave the Torah to the Jewish nation with Chesed. The same when we give Zedakah (Charity). We should use our right hand because we give the money with Chesed and not with Judgment !
This could also be the reason why a Jew is handing over a Torah scroll by using his right hand and the recipient is using his right hand.