Zevachim 9:4-5

Zevachim 9:4

Just as the unfit animals (in 9:2) are not brought down from the altar, they are not brought back up to the altar if brought down. All of these animals are brought down if they were brought up to the altar alive. A burnt offering that was brought up the altar alive must be brought down; if it was slaughtered on top of the altar, the kohein must skin it and cut it up there.

Zevachim 9:5

The following, if brought up the altar, are brought down: the flesh of kodshei kodashim and kodshim kalim (sacrifices of greater and lesser sanctity, respectively, which are meant to be eaten rather than burned), the remainder of the omer of barley brought on 16 Nisan, the two loaves brought on Shavuos, the showbread, the remainder of flour offerings, and incense. The wool on the heads of lambs brought as burnt offerings, the beards of goats and the bones, tendons, horns and hoofs of burnt offerings go up on the altar if they are still attached as per Leviticus 1:9, “the kohein shall burn everything on the altar.” If they were separated, they do not go up as per Deuteronomy 12:27, “you shall offer your burnt offerings; the meat and the blood.”