Tribunals can handle processes in addition to marriage nullity causes. It is the church's court. Although it functions differently than civil courts, it can handle a variety of matters just like civil courts.
It can handle disputes (e.g., a secretary alleges that she was unjustly fired by a pastor). This is not common due to the fact that people don't know this, usually if they think of taking legal action they go to a civil court, plus the diocesan tribunal does not have any real enforcement ability except against clergy or religious.
The tribunal can handle penal processes. For example, it can process a dismissal from the clerical state (e.g., if a priest is accused of sexual abuse of a minor) or it can impose an excommunication.
This is the basic process for handling a penal matter:
1. A preliminary investigation is conducted by a local ordinary (by the bishop, vicar general, or another episcopal vicar). This does not mean that the ordinary must conduct it personally, only that he oversees it. An ordinary exercises executive power.
2. Canon 1722 states: "To prevent scandals, to protect the freedom of witnesses, and to guard the course of justice, the ordinary, after having heard the promoter of justice and cited the accused, at any stage of the process can exclude the accused from the sacred ministry or from some office and ecclesiastical function, can impose or forbid residence in some place or territory, or even can prohibit public participation in the Most Holy Eucharist." It seems that this canon in part has been invoked in what the diocese is calling "administrative leave."
3. Once the preliminary investigation is concluded, then the ordinary must determine how to proceed: whether to dismiss the accusations, whether to impose a penalty or some lesser penance or warning by executive power, or whether a judicial process must be initiated.
4. If the ordinary decides that a judicial process must be initiated, then he must direct the promoter of justice to initiate a tribunal process. Only at this stage is the tribunal involved. The promoter of justice functions as the petitioner and the accused as the respondent. Three judges must serve in the process with one of them as presiding judge.
5. The tribunal then accepts the promoter of justice's petition, cites the respondent, determines the joinder of issues, and gathers evidence (in addition to whatever was gathered in the preliminary investigation). The tribunal must be careful to protect the right of the accused to defend him or herself. All of this takes time.
6. Finally, the tribunal reaches a decision and either dismisses the process or imposes a penalty.
With Msgr. McAuliffe, it seems that they are still at the stage of the preliminary investigation. What is unclear is, if theft has taken place, whether the police will also be involved. What typically happens is that when criminal actions are taken by civil authorities, usually the ecclesiastical process is put on hold until the civil process is complete. Often, the results of the civil criminal investigation is taken as evidence in the tribunal process.
