"It is permissible to kill a criminal if this is necessary for the welfare of the whole community. " ST IIa-IIae, q. 64, a. 3
Thus the death penalty is allowed, if and only if, it is necessary to safeguard the community, not because a criminal "deserves" it. This is what the Church still teaches in the CCC:
"the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor." CCC 2267
This is allowed because of the Catholic doctrine of double effect - we do not will a violation of the Fifth Commandment, it is just an unavoidable consequence of having to protect lives. And if it is possible to protect the community without killing, the State must not use the death penalty
"If, however, non-lethal means are sufficient to defend and protect people's safety from the aggressor, authority will limit itself to such means" CCC 2267
Thus the fact that the death penalty is allowed when it is absolutely necessary and unavoidable to protect people from a dangerous criminal, is not a justification for its use merely as a form of punishment, since it does not meet the criteria for double effect when it is not unavoidably necessary.
Thus a Catholic can support the death penalty only if he believes it will be used only when absolutely necessary to protect society - if he supports it in other cases, logically he denies the right to life. In the United States, life imprisonment is cheaper to the taxpayer than the death penalty, no prisoner has ever escaped from a Federal super-max prison, and we have several proven cases of wrongful execution. So when we killed an innocent man recently when it would have been cheaper to imprison him for life, how is it not murder?
Especially in California, where all we need is a voter proposition to eliminate the death penalty system that costs $114 million over and above just keeping them locked up for life? Why are we Catholics not at the forefront of the effort to eliminate this evil?