The Ruling Applies on Shabbos and Yom Kippur
The prohibition on carrying in Crown Heights applies on both Shabbos and Yom Kippur. This is stated expressly in Crown Heights Beis Din material before the public eruv dispute of 2016, in the signed rulings issued during 2016, and again in the ruling published for residents and visitors in Tishrei 5786.
Yom Kippur therefore cannot be treated as though the question of the Crown Heights eruv concerns Shabbos alone. Where the local rulings prohibit carrying in the neighborhood, they apply the prohibition to Yom Kippur as well.
The Tishrei guidance already said so explicitly
In its Tishrei 5776 practical guidance for guests, the Crown Heights Beis Din included a short notice that could hardly be more direct:
Here in the neighborhood there is no eruv, and it is forbidden to carry on Shabbos and on Yom Kippur. On Yom Tov it is permitted to carry, but only things that are needed.
The same visitor notice appears again in the Hebrew Tishrei 5777 guide. Its wording is useful because it places Shabbos, Yom Kippur, and Yom Tov beside one another. It does not treat all three days alike. It specifically says that there is no eruv in the neighborhood and that carrying is forbidden on Shabbos and Yom Kippur, while Yom Tov has its own rules concerning carrying for a need.
The Tishrei 5776 guidance appears in the Crown Heights chronology together with the later signed rulings.
The signed Sivan ruling includes Yom Kippur in the psak
The ruling issued in Sivan 5776 and signed by Rabbi Avrohom Osdoba and Rabbi Shlomo Yehuda Halevi Segal addresses Anash, guests, and residents of Crown Heights. After stating that there is no halachically valid eruv within the neighborhood, it says:
It is therefore forbidden for every man and woman, and for the members of their households, to carry out or bring in and to carry from one domain to another. Carrying is forbidden on holy Shabbos and on Yom Kippur, in accordance with the law of our holy Torah.
This is not an inference from the general halachos of Yom Kippur. Yom Kippur is named in the text of the Crown Heights ruling itself.
Read the Sivan 5776 ruling in full.
The 2 Iyar ruling's reference to Shabbos does not narrow the other rulings
The 2 Iyar 5776 Beis Din notice, signed by Rabbi Aharon Yaakov Schwei and Rabbi Yosef Yeshaya Braun, says that “on Shabbos it is absolutely forbidden to carry in the streets of the neighborhood.” That notice was answering the immediate question of the newly publicized eruv and states its practical conclusion in terms of Shabbos.
It should not be read as creating a distinction under which carrying becomes permitted on Yom Kippur. The Beis Din's Tishrei guidance had already named Yom Kippur, the Sivan 5776 ruling expressly named Yom Kippur, and the later Tishrei 5786 ruling did so again. The documents are complementary on this point.
The Tishrei 5786 ruling repeats both days
On 4 Tishrei 5786, Rabbi Avrohom Osdoba and Rabbi Yosef Yeshaya Braun issued a signed ruling addressed to “the residents of our neighborhood and the visitors.” It begins:
In light of misleading notices concerning carrying in our neighborhood on Shabbos Kodesh and Yom Kippur, we hereby republish a ruling that was issued previously:
Within the Crown Heights neighborhood and its vicinity, it is forbidden to carry in a public domain and to transfer from one domain to another in any manner on Shabbos Kodesh and Yom Kippur.
The timing and addressees make the practical purpose plain. Crown Heights receives many guests during Tishrei, and the ruling tells residents and visitors that the local prohibition on carrying remains in force on Yom Kippur as well as Shabbos.
Read the 4 Tishrei 5786 ruling in full.
Yom Kippur has its own practical halachos
The fact that the Crown Heights ruling applies on Yom Kippur settles the local eruv question, but it does not replace the full halachos of carrying on Yom Kippur. Questions involving medicines, medical devices, mobility, children, or other special circumstances may involve additional halachic considerations.
The dedicated page on carrying on Yom Kippur in Crown Heights treats those halachos in their own setting. For the rulings discussed here, the central fact is explicit: the Crown Heights Rabbonim prohibit relying on the advertised eruv for carrying on both Shabbos and Yom Kippur.