§1. The judicial confession of one party relieves the other parties from the burden of proof if it concerns some private matter and the public good is not at stake.
§2. In cases which regard the public good, however, a judicial confession and declarations of the parties which are not confessions can have a probative force which the judge must evaluate together with the other circumstances of the case; the force of full proof cannot be attributed to them, however, unless other elements are present which thoroughly corroborate them.
Source: Code of Canon Law (Vatican.va)