Anytime a Zion society is established the law of consecration will be a part of it. This was true for the City of Enoch and it was true for a period of time with the Nephites after Christ appeared to them though in the Book of Mormon it is spoken of as having their things in "common." This existed for quite a while and then we read in 4 Nephi
24 And now, in this two hundred and first year there began to be among them those who were lifted up in pride, such as the wearing of costly apparel, and all manner of fine pearls, and of the fine things of the world.
25 And from that time forth they did have their goods and their substance no more common among them.
After this point I imagine they probably did live the law of tithing or something like it though the scriptures are silent on the matter.