If a person is found murdered in between two cities, the court measures to see which city is closer to the deceased. The elders of that city then hold a ceremony in which they break the neck of a calf. They wash their hands and declare that their city is not responsible for the victim's death.
The ceremony was not conducted if the victim was found near Jerusalem (which did not belong to any of the Tribes) or near a city whose inhabitants were mostly non-Jews. Also, proximity was not the sole deciding factor in determining the city to conduct the ceremony; population was also a factor. (See Talmud Baba Basra 23b.)
This is a shocking thing to do - which is exactly why it's done. This ceremony attracts the attention of the citizens. When they see the elders of the city - prominent, learned men - take a calf down to the river and break its neck, it's certainly disturbing. This is meant to stir the hearts of the people to remove such evil as bloodshed from their midst.
This mitzvah applies at a time when the Jews reside in their land. It is discussed in the Talmud in tractate Sotah on pages 44b-47b and in Kerisus on 26a. It is codified in the Mishneh Torah in the ninth chapter of Hilchos Rotzeiach. This mitzvah is #181 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.