§1. The conference of bishops can compile a list of censors outstanding in knowledge, correct doctrine, and prudence to be available to diocesan curias or can also establish a commission of censors which local ordinaries can consult; the right of each local ordinary to entrust judgment regarding books to persons he approves, however, remains intact.
§2. In fulfilling this office, laying aside any favoritism, the censor is to consider only the doctrine of the Church concerning faith and morals as it is proposed by the ecclesiastical magisterium.
§3. A censor must give his or her opinion in writing; if it is favorable, the ordinary, according to his own prudent judgment, is to grant permission for publication to take place, with his name and the time and place of the permission granted expressed. If he does not grant permission, the ordinary is to communicate the reasons for the denial to the author of the work.
Source: Code of Canon Law (Vatican.va)