"As the Parliament's resolution rightly stresses, respect for the rule of law is essential for the functioning of the Union. That being said, the rule of law also requires respect for the competences of the member states and the choices made by them in the exercise of their exclusive competences," the bishops wrote.
They said that the resolution also appeared to question the right to conscientious objection.
"This is particularly worrying considering that in the healthcare sector conscientious objectors are in many cases subject to discrimination. In our view, such unjust stigmatization should not be promoted," they said.
They added: "In regard to the right to conscientious objection, the European Union Charter entails the need to respect national constitutional traditions and the development of national legislation on the issue."
The bishops also expressed concern that the principle of "non-discrimination," highlighted in the resolution, could be used to "stretch or blur the limits" of the EU's authority over member states.
COMECE, founded in 1980, consists of bishops delegated by the bishops' conferences of the 27 member states of the European Union. The letter was signed by COMECE's president Cardinal Jean-Claude Hollerich of Luxembourg; Bishop Mariano Crociata of Latina, Italy; Bishop Franz Josef Overbeck of Essen, Germany; Bishop Noel Treanor of Down and Connor, Northern Ireland; and Bishop Jan Vokal of Hradec Králové, Czech Republic.
In the letter, the bishops alluded to mass protests in Poland in the wake of the Constitutional Tribunal's ruling. Demonstrators disrupted Masses while holding signs supporting abortion, left graffiti on Church property, vandalized statues of St. John Paul II, and chanted slogans at clergy.
The bishops said: "We also noted with sadness that no condemnation or solidarity was expressed in the text with regard to the unacceptable attacks on churches and places of worship in the context of protests related to this law in Poland."