Q. Someone carrying a Sefer Torah to the bimah tripped and fell. To protect the Sefer he was able to maneuver to fall on his side, and the Torah did not touch the ground. He was also wearing tefilin and the side of his head was on the floor, but again, the tefilin didn’t touch the ground. Does he or others present have to fast?

A. In regards to the Sefer Torah itself Har Tzvi (1: 40) maintains that he does not have to fast, as long as even the eitz chaim did not touch the ground. He suggests that some tzedaka should be donated by the one that fell.
In regards to the tefilin shel rosh, since they also did not touch the ground, Rivavos Efraim (1: 30), rules that since they didn’t touch the ground no taanis is necessary. (See also Piskei Teshuvos O.H. 40: 3, and 2 n. 4).
Horav Shlomo Miller’s Shlit”a opinion is that he does not have to fast, even if the retzuah of the head touched the floor. If possible he should donate to tzdaka.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a