The matter of fasting if a sefer Torah is dropped is mentioned in the Magen Avraham[1] in the name of Mishpetei Shmuel. They describe it as a custom that had been widely accepted, for which they sought a basis. It is fitting, in our view, that because of the emotions involved, practice on this matter has developed in a “beyond-the-letter-of-the-law” and perhaps “grass-roots” manner, rather than through clear halachic dictate. Some poskim indicate that the matter is best to be decided by the local rabbi, based on what he deems as an appropriate reaction for his community.[2] We will cite the source for a related practice, which, we believe, is somewhat related to the situation about which you ask.
The gemara[3] states that one must rip his garment if he sees a Torah or tefillin being destroyed. As destruction is more severe than falling, our minhag relates only to fasting, which would be less intense a sign of remorse than ripping one’s garment. We will concentrate on a fallen sefer Torah, which, being holier than tefillin, is more serious in several ways, including the effect as regards onlookers.
Most rule that only the one who dropped the Torah must fast.[4] Others say that all who were present when the sefer Torah fell may share a collective negligence and must fast.[5] Some say that the concern at hand is the bad omen for all those who were, for whatever reason, connected to the event. This concern could extend to those who saw the Torah fall[6] or even to the whole community.[7]
As to the number of fast days, most opinions state that one day is sufficient, but others suggest fasting Monday-Thursday-Monday or even forty days. The minimum step to be taken is that the one who dropped the sefer Torah should fast one day. We suggest the following for those who want to take a more stringent yet mainstream approach to deal with the traumatic occurrence. The person who dropped the Torah should fast Monday-Thursday-Monday. If it is difficult for him, he can redeem his fast with tzedaka (while trying to fast at least once). It is also nice to donate something to beautify the Torah that fell. Onlookers should fast one day, and, if this is difficult, they can redeem the obligation with tzedaka. These suggestions are consistent with the analysis of the Tzitz Eliezer[8] and Igrot Moshe.[9] If the local rabbi has decided on additional steps, they should be followed.