An article in Periodica, the canon law journal of the Gregorian University in Rome, was released just this morning that answers the question. The full article is behind a paywall, but I hope that it spreads widely, given how important this right is, especially in these days and especially in the USA. Here is the abstract:
The venerable right against self incrimination — nemo tenetur prodere seipsum — has long been recognized in both canon law (cf. can. 1728 §2) and in secular juridical systems. In the current environment, however, a priest’s right to remain silent has been jeopardized, in practice, at least in the Church. This article discusses the basis for the right, examines its use outside of judicial processes (including preliminary investigations [cf. can. 1717]), and raises the question of whether an ecclesial version of the famous Miranda warning has become necessary, and the possible implications of its implementation.