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This Sabbath is also called the Sabbath (of the red cow)Parah. We find it in Numbers (Bamidbar) chapter (perek) 19, yud tes. Any person, who would touch the corps of a human, would sprinkle himself/herself with the ashes of the cow. If a person touched someone with a sword (killed them in war through a sword), human bone, open grave site (war) they would be unclean for seven days. A clean person will sprinkle the unclean person with some of the dust from red cow filled with water from a running spring. If a person touches such a person who was unclean will also become unclean.
The red cow was not easy to find. It could not contain any blemishes, never had a yoke on it (it didn't work) and had to be completely red in color.