In the previous Halacha we have established that one may not hang up wet clothing on Shabbat in order to dry it. This is not a Torah prohibition; rather, our Sages prohibited this so that people do not suspect the individual hanging up the clothes on Shabbat that he laundered them on Shabbat.
Let us now discuss whether or not it is prohibited to hang up dry clothing on Shabbat.
Indeed, Rabbeinu Yosef Haim is of the opinion that it is likewise forbidden to hang up dry clothing on a clothes line on Shabbat, for the people seeing the individual do this do not know whether or not the garment is dry or wet and they will certainly suspect him of laundering on Shabbat or people will suspect that the garment was only partially laundered, i.e. it had a stain on it and this person only washed that stain and then hung it up. The great Rishon Le’Zion Hagaon Harav Yitzchak Yosef Shlit”a ruled likewise may years ago in his Sefer Yalkut Yosef, Volume 3 that one may not hang up even completely dry clothing on Shabbat out of concern of suspicion.
Maran zt”l’s Question on Rabbeinu Yosef Haim
Nevertheless, Maran Rabbeinu zt”l questions the opinion of Rabbeinu Yosef Haim in his Halichot Olam, Volume 3 based on the Magen Avraham who writes that only when the clothing is completely wet is it forbidden to spread them out to dry; however, if the clothing is not wet, our Sages never forbade spreading it out to dry on Shabbat and this was not included in their original decree. Many other great Acharonim concur and write that although there is room to prohibit hanging up a garment which is wet in only a small portion of the garment, nevertheless, if the garment is completely dry, there is no prohibition to spread it out or hang it up on Shabbat, even if this is being done in the same manner one spreads clothing out to dry.
This can further be inferred from the words of the Gemara, “One may not spread out one’s clothing on Shabbat even (to dry them) from sweat.” This would imply that only if the clothes are partially wet is it forbidden to spread them out; however, if they are not wet at all, there is no prohibition to do so. Nevertheless, if one acts stringently out of concern for the opinion of the Ben Ish Hai and hangs them up in a manner in which it is noticeable that one does not intend to dry the garments, one is especially praiseworthy.
Summary: One may hang up completely dry clothing on Shabbat.