§1. A perpetually professed religious is not to request an indult of departure from an institute except for the gravest of causes considered before the Lord. The religious is to present a petition to the supreme moderator of the institute who is to transmit it along with a personal opinion and the opinion of the council to the competent authority.
§2. In institutes of pontifical right, an indult of this type is reserved to the Apostolic See. In institutes of diocesan right, however, the bishop of the diocese in which the house of assignment is situated can also grant it.
Source: Code of Canon Law (Vatican.va)