Under what conditions might a priest refuse the sacrament of matrimony to a couple?

Answer 1

If one or both of them are not of the same religious beliefs of the Priest. If the marriage is just wrong, for the wrong reasons, or dangerous.

If they weren't both of the Christian faith or if one of the persons was still married.

Answer 2

A couple seeking to marry in the Catholic Church can only do so if they are both free to enter into marriage. A priest cannot perform a wedding ceremony if one or both of the parties seeking to marry are not free to do so. Therefore a priest will not marry a couple if one or both is not free to enter into marriage.

Canon Law spells out a whole list of impediments to marriage. Some impediments can be dispensed with as they are of ecclesiastical origin, others are of Divine origin, and therefore cannot be dispensed. The following are a list of impediments:

Age: A man under 16 years, and a women under 14 years cannot validly marry because they lack the emotional capacity and maturity to enter into a marital contract

Impotence: If one of both of the spouses is impotent and the condition is permanent (can never be medically corrected.)

Previous Marriage: One who is divorced but did not seek and receive an annulment is not free to marry.

Disparity of Cult: This is a marriage between a Catholic baptized party and a unbaptized party. Without a dispensation, a priest cannot marry the couple.

Sacred Orders: A priest who left the priesthood cannot marry without a dispensation from the Holy See.

Vow of Chastity: One who has made solemn vows (A religious) but leaves the order cannot marry without a dispensation from the Holy See.

Abduction: One cannot kidnap another party and force them to marry. One must enter into marriage freely.

Crimen: One or both of the parties cannot murder the spouse of another then seek to marry them. Interestingly enough this can be dispensed and I am not sure why, but it probably has to do with some obscure something or other that happened in history.

Consanguinity: You cannot marry someone closely related to you by blood- such as your sister.

Affinity: Parties related by marriage in a prohibited degree.

Catholics are bound by Sacramental Form. This means that if a Catholic attempts to marry outside the Church without a dispensation the marriage is invalid.

Non-Catholics are not bound by sacramental form.

In any case priests cannot marry those who are not free to Marry unless or until the impediment (thing standing in the way of the marriage) is resolved.

Answer 3

A Catholic Priest is permitted to perform the nuptials of two individual Catholics, or that in which only one of the parties is Catholic. A priest may not perform the marriage of two non-Catholics. [I am a Priest, and personally] I discourage marriage in the Church if the Catholic party(ies) do not practice the faith -- they want pretty pictures. If the couple is already living together. Should a child be involved, and the parties were trying their best to practice their faith, I would first investigate to assure myself that they "freely" wish to marry. In all cases there assurance must be obtained that the children would be baptized and educated in the Roman Catholic Faith.