Cedar's first article separates the true cedar of Lebanon from the North American red cedar sold under the same name. The peoples who actually burned each tree developed purification rites independently of one another, with no shared source and no contact, and the parallel is worth more than the shared word.
The Hebrew Bible uses true cedar, Cedrus libani, in a specific purification rite for a healed skin affliction at Leviticus 14, alongside hyssop and scarlet thread, a ritual use distinct from its better known role as Solomon's Temple timber; cedar here functions as a cleansing agent in law, not only as fine building material.
An ocean and several thousand years away, numerous peoples of the northern and plains regions of North America burn Juniperus virginiana, the tree that carries the cedar name without the botany, as a purifying smoke central to the sweat lodge and to other ceremonial cleansing practice. As with sage and other North American plant medicine described elsewhere on this site, that specific ceremonial use belongs to the peoples who practise it rather than to a general technique available to anyone who burns the wood.
Two purification traditions, one Levitical and textual, one oral and still living, arrived at the same basic act, cedar smoke against contamination, from trees that are not even the same genus, joined only by a common name inherited from a mistaken botanical identification made centuries after both practices were already old.