The answer to this, as with almost all answers on the Third Reich, is complicated.

German Catholics

If you were an ordinary Catholic citizen of the Reich, you were in very little danger other than that of any other citizen. You would not have been targeted due to your religious identity.

If you were a Catholic clergyman, you would have been in an interesting position. During the pre-war years of Nazi rule, especially between 1936-1937, there was something called the Kirchenkampf or "Church Struggle." In it, some of the higher ranking Nazis, Goebbels and Rosenberg in particular, attempted to "coordinate" the churches (both Catholic and Protestant) under the influence or authority of the Nazis. They had successfully "coordinated" most systems and structures of Germany and the Churches were valuable because they could serve as bases of power with different appeal than those of other systems. However, both churches demonstrated themselves to be unwilling to compromise their own independence (although they did make some compromises to the regime in order to maintain that independence).

As stated above, this situation in which the Nazis attempted to gain power over the Catholic church occurred off and on throughout the period of Hitler's time in power. Hence, if you spoke out in opposition to these attempts it was possible that you might be arrested, tried (in courts controlled by the Nazis), and detained in camps. Additionally, if you spoke out against other aspects of Nazi rule, you might also be detained. This, however, was no different than other citizens who spoke out.

What this tells us then, is that Catholics were not persecuted as such, but only when they overstepped into opposition to the Nazis. Additionally, they were not subject to exterminatory actions such as the Jews and Roma/Sinti were. They often died or were killed in concentration camps, but they were not sent to death camps for extermination nor were they shot in open air massacres.

Polish Catholics

Being a Polish Catholic clergyman was a whole different situation. Following the swift defeat of Poland, the Nazis implemented a brutal treatment of the population there. Specifically Reinhard Heydrich called for killing the Jews, nobility and clergy and many in the military seemed to know that such killings were taking place.

The clergy were being targeted because they were leaders in Poland. As such they were potential leaders of resistance to German occupation. Clergy were specifically targeted in two organized assaults: Intelligenzaktion & Aktion A-B. Both attempted to rid the Poles of any leadership and also saw mass extermination of Jews along with the Polish intelligentsia and clergy.

Source

Kershaw, Ian. Hitler: 1936-1945 Nemesis. New York: W.W. Norton, 2000.

Noakes, J. & Pridham, G. Nazism: 1919-1945 Volume 3: Foreign Policy, War and Racial Extermination. Exeter, University of Exeter Press, 1988.