As is known, if a Sefer Torah falls on the floor (even if it's covered) there is a halacha that one must fast. (See this question and answer for many sources on this topic.) What about in a case when Navi or Kesuvim that was written on klaf fell on the floor (either when it was covered or not covered it -- if there is any difference in regards to Navi/Kesuvim)?
As noted in the linked question, the source of the minhag is from Mishpetei Shemuel 12. He brings a saying of the people (quoted in Shulchan Aruch OC 288:5) that one must fast if he sees a Torah burnt in his sleep. He extends this rule to fasting when a Torah is dropped by his own logic, and then extends it again to tefillin being dropped based on a gemara (Moed Kattan 26a) which says that if a Torah or tefillin is forcefully burnt one must rend one's clothes. As the Rosh (Moed Katan 3:64, ruled in Shulchan Aruch YD 340:37) extends the requirement of clothes-rending to even "one parsha from Nevi'im or Ketuvim", it would seem that the Mishpetei Shemuel's logic follows here as well.