Zevachim 16: Impure or Blemished; Performing Ritual Rites

The rabbis discuss the implications of a priest who is impure continuing to perform the sacrificial rites.  They consider a number of factors including whether priests are similar to common people when and how the can practice sacrifice.  What counts as 'desecration' in public altars and in Temple sacrifices.  The acute mourner, whether a priest or someone else, is prohibited from performing sacrificial rites.

In amud (b), the rabbis confirm that there are differences by tribe and by state of acute mourning.  The Gemara identifies the one limitation on the actions of a blemished priest.  That is the priest's ability to impart ritual impurity upon others through touch.  An ordinary priest who is blemished is permitted to perform a communal offering.