Assuming that the guilty party’s identity and responsibility have been fully determined, the traditional teaching of 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.
If, however, non-lethal means are sufficient to defend and protect people’s safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity to the dignity of the human person.
Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm – without definitely taking away from him the possibility of redeeming himself – the cases in which the execution of the offender is an absolute necessity “are very rare, if not practically nonexistent.”
The Catechism of the Catholic Church, 2267

Ellen Kolb reports on her website Leaven for the Loaf that the NH House Criminal Justice and Public Safety committee has recommended a repeal of the death penalty as “ought to pass” thanks to the change of heart by long-time death penalty supporter Representative David Welch, the ranking Republican on the committee.
Often thought of as a liberal position, I make the argument that a little “l” liberal society with full ability to imprison a dangerous criminal, thereby protecting human life, needs to only kill criminals if it means to be barbaric. From a public safety point of view, the death penalty saves no lives and only serves to take another one. From crime deterrent point of view, I can’t fathom a situation where a capital crime is about to happen and the potential criminal stops and says, “Nah. I’m not going to do this. Not because I respect the person’s inherent right to live, but because I’m afraid of losing my inherent right to live.” From a budgetary point of view, it costs a lot of money since we rightly give the condemned every reasonable opportunity to make their case for living, since our justice system is based on convicting as many guilty parties as possible while (hopefully) convicting zero innocent parties.
God of Eden and of our mothers, please help the New Hampshire legislature see that we are all made in your image, and that your love for each and every one of us does not diminish no matter how grave our sins. Bless us with wisdom and compassion. In Jesus’ holy name, in the Father, through the Holy Spirit. Amen.