A council of Carthage (418 – 419) approved the following canon:

That whosoever says that Adam, the first man, was created mortal, so that whether he had sinned or not, he would have died in body— that is, he would have gone forth of the body, not because his sin merited this, but by natural necessity, let him be anathema.

The council of Orange in 529 published the following:

CANON 1. If anyone denies that it is the whole man, that is, both body and soul, that was “changed for the worse” through the offense of Adam’s sin, but believes that the freedom of the soul remains unimpaired and that only the body is subject to corruption, he is deceived by the error of Pelagius and contradicts the scripture which says, “The soul that sins shall die” (Ezek. 18:20); and, “Do you not know that if you yield yourselves to anyone as obedient slaves, you are the slaves of the one whom you obey?” (Rom. 6:16); and, “For whatever overcomes a man, to that he is enslaved” (2 Pet. 2:19).

CANON 2. If anyone asserts that Adam’s sin affected him alone and not his descendants also, or at least if he declares that it is only the death of the body which is the punishment for sin, and not also that sin, which is the death of the soul, passed through one man to the whole human race, he does injustice to God and contradicts the Apostle, who says, “Therefore as sin came into the world through one man and death through sin, and so death spread to all men because all men sinned” (Rom. 5:12).

These canons are concerned with establishing that original sin affects man spiritually, but nevertheless they take it as an absolute fact that bodily death is a result of sin.

The council of Trent published these canons:

1. If any one does not confess that the first man, Adam, when he had transgressed the commandment of God in Paradise, immediately lost the holiness and justice wherein he had been constituted; and that he incurred, through the offence of that prevarication, the wrath and indignation of God, and consequently death, with which God had previously threatened him, and, together with death, captivity under his power who thenceforth had the empire of death, that is to say, the devil, and that the entire Adam, through that offence of prevarication, was changed, in body and soul, for the worse; let him be anathema.

2. If any one asserts, that the prevarication of Adam injured himself alone, and not his posterity; and that the holiness and justice, received of God, which he lost, he lost for himself alone, and not for us also; or that he, being defiled by the sin of disobedience, has only transfused death, and pains of the body, into the whole human race, but not sin also, which is the death of the soul; let him be anathema:–whereas he contradicts the apostle who says; By one man sin entered into the world, and by sin death, and so death passed upon all men, in whom all have sinned.

Apparently there was an original formulation of the first canon which specified that the death with which man had been threatened was a bodily death, but this specification was omitted in the final formulation. There is some discussion of this issue here. Regarding this point, the author of the essay concludes, “At any rate it does not seem that we can say for certain that Trent is here defining immortality as a gift to man before sin and simple physical death as a punishment for sin.” Nonetheless, the council certainly seems to take for granted that man without sin would not have physically died.

The Second Vatican Council stated in the document Gaudium et Spes,

18. It is in the face of death that the riddle a human existence grows most acute. Not only is man tormented by pain and by the advancing deterioration of his body, but even more so by a dread of perpetual extinction. He rightly follows the intuition of his heart when he abhors and repudiates the utter ruin and total disappearance of his own person. He rebels against death because he bears in himself an eternal seed which cannot be reduced to sheer matter. All the endeavors of technology, though useful in the extreme, cannot calm his anxiety; for prolongation of biological life is unable to satisfy that desire for higher life which is inescapably lodged in his breast.

Although the mystery of death utterly beggars the imagination, the Church has been taught by divine revelation and firmly teaches that man has been created by God for a blissful purpose beyond the reach of earthly misery. In addition, that bodily death from which man would have been immune had he not sinned (cf. Wis. 1:13; 2:23-24; Rom. 5:21; 6:23; Jas. 1:15.) will be vanquished, according to the Christian faith, when man who was ruined by his own doing is restored to wholeness by an almighty and merciful Saviour. For God has called man and still calls him so that with his entire being he might be joined to Him in an endless sharing of a divine life beyond all corruption. Christ won this victory when He rose to life, for by His death He freed man from death. Hence to every thoughtful man a solidly established faith provides the answer to his anxiety about what the future holds for him. At the same time faith gives him the power to be united in Christ with his loved ones who have already been snatched away by death; faith arouses the hope that they have found true life with God.

The document thus says explicitly that man would have been free of bodily death if he had not sinned. This passage is quoted by the Catechism of the Catholic Church:

Death is a consequence of sin. The Church’s Magisterium, as authentic interpreter of the affirmations of Scripture and Tradition, teaches that death entered the world on account of man’s sin. Even though man’s nature is mortal God had destined him not to die. Death was therefore contrary to the plans of God the Creator and entered the world as a consequence of sin. “Bodily death, from which man would have been immune had he not sinned” is thus “the last enemy” of man left to be conquered.

This is repeated in the “In Brief” section, summarizing, “As a consequence of original sin, man must suffer ‘bodily death, from which man would have been immune had he not sinned’ (GS § 18).”

The Catechism does not always contain specifications such as “The Church’s Magisterium, as authentic interpreter of the affirmations of Scripture and tradition,” before going on to make a statement. The purpose of this addition seems to be to recognize that some suppose that bodily death is not a result of sin, and to exclude this possibility, more or less completely. Fr. Zimmerman’s book, Original Sin: Where Doctrine Meets Science, was published about a year and a half before the publication of the Catechism. It is not impossible that the authors of the text of the Catechism were thinking of his opinion in particular.