Here are the relevant excerpts from Evangelium Vitae
55. This should not cause surprise: to kill a human being, in whom the image of God is present, is a particularly serious sin. Only God is the master of life! Yet from the beginning, faced with the many and often tragic cases which occur in the life of individuals and society, Christian reflection has sought a fuller and deeper understanding of what God's commandment prohibits and prescribes.(43) There are in fact situations in which values proposed by God's Law seem to involve a genuine paradox. This happens for example in the case of legitimate defence, in which the right to protect one's own life and the duty not to harm someone else's life are difficult to reconcile in practice. Certainly, the intrinsic value of life and the duty to love oneself no less than others are the basis of a true right to self-defence. The demanding commandment of love of neighbour, set forth in the Old Testament and confirmed by Jesus, itself presupposes love of oneself as the basis of comparison: "You shall love your neighbour as yourself " (Mk 12:31). Consequently, no one can renounce the right to self-defence out of lack of love for life or for self. This can only be done in virtue of a heroic love which deepens and transfigures the love of self into a radical self-offering, according to the spirit of the Gospel Beatitudes (cf. Mt 5:38-40). The sublime example of this self-offering is the Lord Jesus himself.
Moreover, "legitimate defence can be not only a right but a grave duty for someone responsible for another's life, the common good of the family or of the State".(44) Unfortunately it happens that the need to render the aggressor incapable of causing harm sometimes involves taking his life. In this case, the fatal outcome is attributable to the aggressor whose action brought it about, even though he may not be morally responsible because of a lack of the use of reason.(45)
56. This is the context in which to place the problem of the death penalty. On this matter there is a growing tendency, both in the Church and in civil society, to demand that it be applied in a very limited way or even that it be abolished completely. The problem must be viewed in the context of a system of penal justice ever more in line with human dignity and thus, in the end, with God's plan for man and society. The primary purpose of the punishment which society inflicts is "to redress the disorder caused by the offence".(46) Public authority must redress the violation of personal and social rights by imposing on the offender an adequate punishment for the crime, as a condition for the offender to regain the exercise of his or her freedom. In this way authority also fulfils the purpose of defending public order and ensuring people's safety, while at the same time offering the offender an incentive and help to change his or her behaviour and be rehabilitated.(47)
It is clear that, for these purposes to be achieved, the nature and extent of the punishment must be carefully evaluated and decided upon, and ought not go to the extreme of executing the offender except in cases of absolute necessity: in other words, when it would not be possible otherwise to defend society. Today however, as a result of steady improvements in the organization of the penal system, such cases are very rare, if not practically non-existent.
In any event, the principle set forth in the new Catechism of the Catholic Church remains valid: "If bloodless means are sufficient to defend human lives against an aggressor and to protect public order and the safety of persons, public authority must limit itself to such means, because they better correspond to the concrete conditions of the common good and are more in conformity to the dignity of the human person".(48)
Hmmm-m-m-m, wonder why popes during the Spanish Inquisition had no problem with this?