The Ruling Applies on Shabbos and Yom Kippur
Carrying in Crown Heights is forbidden on Yom Kippur as well as Shabbos. A machzor, tallis, key, medication, or other needed object should be placed where it will be used before the fast begins.
Shabbos and Yom Kippur
The joint ruling of Rabbi Avrohom Osdoba and Rabbi Shlomo Yehuda Halevi Segal prohibits carrying on Shabbos and Yom Kippur throughout Crown Heights. The official Beis Din guidance and the public instruction issued before Yom Kippur 5786 give the same direction.
Hotza'ah is among the melachos forbidden on Yom Kippur. The fast and the special tefillos do not change the status of the streets or make a mitzvah object permissible to carry.
A machzor and tallis can be brought to shul before Yom Kippur. Keys, medication, children's needs, and other necessities can likewise be placed at their destination in advance. Arrangements involving illness or danger follow their own halachos and should be made according to the actual need.
Mitzvah use does not permit carrying
A machzor, tallis, or food needed after the fast may be essential to the day, but a mitzvah or practical need does not by itself permit hotza'ah. The same applies to an object carried only from one nearby building to another.
The ordinary plan in Crown Heights is therefore the same as on Shabbos: do not rely on the publicized eruv, and place needed items where they belong before the day begins.