This is from the Code of Canon Law:
Can. 1142 For a just cause, the Roman Pontiff can dissolve a non-consummated marriage between baptized persons or between a baptized party and a non-baptized party at the request of both parties or of one of them, even if the other party is unwilling.
Can. 1143 §1. A marriage entered into by two non-baptized persons is dissolved by means of the pauline privilege in favor of the faith of the party who has received baptism by the very fact that a new marriage is contracted by the same party, provided that the non-baptized party departs.
§2. The non-baptized party is considered to depart if he or she does not wish to cohabit with the baptized party or to cohabit peacefully without affront to the Creator unless the baptized party, after baptism was received, has given the other a just cause for departing.
Can. 1144 §1. For the baptized party to contract a new marriage validly, the non-baptized party must always be interrogated whether:
1/ he or she also wishes to receive baptism;
2/ he or she at least wishes to cohabit peacefully with the baptized party without aVront to the Creator.
§2. This interrogation must be done after baptism. For a grave cause, however, the local ordinary can permit the interrogation to be done before baptism or can even dispense from the interrogation either before or after baptism provided that it is evident at least by a summary and extrajudicial process that it cannot be done or would be useless.
Can. 1145 §1. The interrogation is regularly to be done on the authority of the local ordinary of the converted party.
This ordinary must grant the other spouse a period of time to respond if the spouse seeks it, after having been advised, however, that his or her silence will be considered a negative response if the period passes without effect.
§2. Even an interrogation made privately by the converted party is valid and indeed licit if the form prescribed above cannot be observed.
§3. In either case, the fact that the interrogation was done and its outcome must be established legitimately in the external forum.
Can. 1146 The baptized party has the right to contract a new marriage with a Catholic party:
1/ if the other party responded negatively to the interrogation or if the interrogation had been omitted legitimately;
2/ if the non-baptized party, already interrogated or not, at first persevered in peaceful cohabitation without aVront to the Creator but then departed without a just cause, without prejudice to the prescripts of cann. ⇒ 1144 and ⇒ 1145.
Can. 1147 For a grave cause, however, the local ordinary can allow a baptized party who uses the pauline privilege to contract marriage with a non-Catholic party, whether baptized or not baptized; the prescripts of the canons about mixed marriages are also to be observed.