When Adolf Hitler came to power in 1933, one of his aims/policies was that of Gleichschaltung, or coordination. The Nazis aimed to eliminate all of the existing power structures in Germany in order to ensure total loyalty to them in the future. All political parties were either banned or voluntarily disbanded themselves, and the formation of new parties was made illegal. Trade Unions were banned at around the same time as the SPD, and replaced with the German Labour Front lead by Robert Ley, a leading Nazi who would later be placed on trial for War Crimes. Youth Groups such as the Scouts were abolished in favour of the Hitler Youth. One of the biggest interest groups in Germany was the Catholic Church. The church presented a double threat to Hitler. First of all, up until fairly recently Catholics had voted in huge numbers for the Centre Party, an explicitly Catholic political party with links to the Church. From this map you can see that the Nazis were especially weak in Catholic dominated areas such as Bavaria, thanks in part to their high levels of support for the Centre Party. Hitler needed to stamp out any remaining fondness that southern Germans had for this party. Additionally, the Catholic Church represented an extra-national alliegance; Catholics who followed the teachings of a foreign Pope could never be fully loyal to Germany in his eyes. Unlike the Protestant Church, who had no international leadership and a less clearly defined hierachy, the Catholic Church could not be controlled simply within Germany. This meant that Hitler needed to treat the Church very carefully, while at the same time trying to wean Catholics away from the Church and towards him. This would be an extraordinarily difficult task, given that 95% of Germans described themselves as belonging to either the Catholic or Protestant churches.

Perhaps recognising the threat posed by the Nazis to the Church, Pope Pius XI negotiated the Reichskonkordat with the Nazis, whereby he agreed to recognise and endorse Hitler as the legitimate ruler of Germany in exchange for concessions, such as allowing Catholic youth groups to continue unobstructed. The Pope also agreed to stop Catholic priests from taking part in explicitly political activities. You can find the full text here in both English and German.

While some see the Konkordat as the Catholic Church simply giving in to Hitler, it was arguably a fairly wise decision, given the extent of Hitler's attacks on other organisations within Germany. By (on paper) ensuring good relationships with the regime, the Catholic Church stood a good chance of weathering the storm and protecting their followers from undue persecution. However, in practice the Nazis took very little notice of the Konkordat, and soon Catholic organisations came under extreme persecution and pressure. For their part as well, some Catholic priests also broke the agreement by openly criticising the regime, most notable Bishop Galens of Münster, who was at the forefront of the public outcry over the euthanasia programme. Arguments about the Konkordat can go both ways. Ultimately the agreement was a canny political move which which went to great lengths to try and protect the followers of the Catholic Church in Germany, but Pius XI was also one of the first international leaders to openly endorse Hitler, and this agreement gave his regime legitimacy.

Ultimately, Pius XI, noting the many breaches of the Konkordat by the Government, issued the Papal Encyclical 'Mit Brennender Sorge', (full text), or 'with burning concern' in 1937, which condemned the Nazi Regime in no uncertain terms and was a significant departure from the previous policy of conciliation. The Pope would also criticise the regime in his Christmas address in 1937. The encyclical was read out in every service on Palm Sunday, thus ensuring that its message was widely distributed across Germany.

This was not the end of persecution of the Church. In response to the encyclical, Churches across the country were raided and all copies seized. Catholic priests and theological students were banned from joining the party in 1937. 455 German born Catholic priests would spend some time in Dachau concentration camp. When the camp was liberated in 1945 there were found to be 1493 Catholic priests from across Europe. It is estimated that up to one third of all priests in Germany were subject to some form of persecution, ranging from arrest to execution. Vast amounts of property was stolen from the Catholic church, although this practice was halted personally by Hitler in 1941.

All in all, the Catholic church were neither passive bystanders nor where they resistance heroes. Individual priests and Catholics offered incredibly brave acts of resistance, such as the aforementioned Bishop Galens. Maximilian Kolbe, a Franciscan friar, offered to die in Auschwitz in the place of a complete stranger. Both of these men were later made Saints. One judge in 1944 shot himself rather than pronounce a death sentence on three Catholic priests he thought were completely innocent. However, there was no organised resistance to the regime from the Church as a whole, what acts of resistance there were, were on the individual level.

Further reading:

For a history of the Centre Party during the Second Reich:

Margaret Anderson, ‘Interdenominationalism, Clericalism, Pluralism: The Zentrumsstreit and the Dilemma of Catholicism in Wilhelmine Germany’. Central European History, Vol. 21, No. 4 (Dec. 1988)

I'm not aware of any books specifically on the role of the Catholic Church during the Nazi Regime, but if you take a look at General Histories of the Nazis in our reading list, most of those will have a chapter or section dedicated to the role of the Church.

Hope this helped, let me know if you have any more questions!

Just a couple additions to the post by /u/Abrytan (no corrections, just some footnote-type material). The Konkordat had been sought for a fairly long time, and the eventual document was pretty similar to the language proposed to the Weimar government. Further, the negotiations were undertaken by Cardinal Secretary of State Eugenio Pacelli. That name is important because he went on to become Pius XI's successor Pius XII. He was also the person largely responsible for the contents of Mit Brennender Sorge (some of my thoughts on that document can be found here. My long post on Pius XII may also be helpful to some. A too-brief summary would be that Pius XII did speak out, but that he did so cautiously and that many did not listen to what he did say. The best nuanced approach to the subject is the biography by Ventresca (I made a post on the Bad History subreddit regarding my opinion that most of the other books are flawed, and the rest of my bibliography can be seen here).

Follow up. Did church in any way assist Nazi higher ups in escaping Europe ? If i remember correctly Argentina was one of the most notable escape zones for this people.

There was a really good post that I saved here a few years ago about Pope Pius XII mostly but does delve into pre world war II. It also has some follow up questions answered by u/Domini_canes.

Here's an article about Pius XII that I read a while back too.