* Church to allow pill that does not induce abortion
* Outcry over church hospitals turning away rape victim
* Bishop promises rape victims will get proper care (Adds critical Catholics, data on church hospitals)
BERLIN, Feb 21 (Reuters) - The Roman Catholic Church in Germany said on Thursday it would permit certain types of "morning-after pill" for raped women, after two hospitals provoked an outcry for refusing to treat a rape victim.
The German Bishops' Conference said church-run hospitals would now ensure proper medical, psychological and emotional care for rape victims - including administering pills that prevent pregnancy without inducing an abortion.
Archbishop Robert Zollitsch said a four-day meeting of German bishops in the western town of Trier had "confirmed that women who have been victims of rape will get the proper human, medical, psychological and pastoral care".
"That can include medication with a 'morning-after pill' as long as this has a prophylactic and not an abortive effect," he said in a statement. "Medical and pharmaceutical methods that induce the death of an embryo may still not be used."
That means there is no change to the Catholic Church's ban on the so-called abortion pill based on the drug mifepristone or RU-486, and marketed as Mifegyne or Mifeprex.
The Church remains firmly opposed to abortion and artificial birth control, but in Germany it will now differentiate between pills that prevent sperm from fertilizing an egg in the womb and pills that induce an abortion, in cases of rape.
The German church, which has already faced mass desertions over cases of sexual abuse of children by priests, had been expected to change its position on the morning-after pill after apologising about an incident involving two hospitals in Cologne last month.
The critical German lay movement "Wir sind Kirche" (We are the Church) said bishops took the decision because they feared losing state subsidies for church hospitals. The Catholic Church runs 25 percent of German hospitals and half of those in North Rhine-Westphalia state, which includes Cologne, it said.
Cologne's Cardinal Joachim Meisner, an ally of the outgoing German-born Pope Benedict, has already apologised for the church hospitals' treatment of the woman. He said it "shames us deeply because it contradicts our Christian mission and our purpose".
The 25-year-old woman was referred to the hospitals by her doctor for a gynaecological exam after she was drugged at a party and woke up on a park bench fearing she had been raped.
The hospitals refused to treat her because they could not prescribe the pill, which is taken after sex to avoid pregnancy. She was eventually treated at a Protestant church-run hospital.
The German bishops' meeting in Trier also tried to address criticism of sexual discrimination by the Church by vowing to include more women in leadership positions, although this will not include the ordination of women as priests.
More than 181,000 German Catholics left the Church in 2010 and a further 126,000 the following year, reducing the total number to 24.47 million in a total population of 82 million. (Editing by Jason Webb)