A 10day baby of my neighbour who is a Christian died, no one could got near the corpse but I did and bury the baby, I want to know the islamic rulings on the rites to give the corpse since the parents are Christians and can we bury in the cementary of Muslims, and if it is baby whose parents are Muslims, do we give the baby Janazah?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

If the situation is as you mentioned in the question that none of the child's guardians buried him [the child], then it is permissible for you to bury him, Allaah willing. It is confirmed in the Sunnah that it is permissible for a Muslim to bury a non-Muslim in case of necessity. For instance, 'Ali buried his father Abu Taalib by order of the Prophet . He also ordered the companions to throw the non-Muslims who were killed in the battle of Badr into a well.

However, a Muslim should not wash a dead non-Muslim as stated by the Maaliki scholars ; this is also the predominant opinion of the Hanbali School. Moreover, it is not permissible for a Muslim to perform a funeral prayer on a dead non-Muslim.

If a Muslim wants to bury the corpse of a non-Muslim, he should not bury him in a Muslim graveyard, because it is not permissible to bury the corpse of a non-Muslim in a Muslim graveyard. Since the parents of the child are Christians, then he follows them in regard to the worldly rulings and so he is a non-Muslim and it is not permissible to bury him in a Muslim graveyard. For more benefit on this matter, please refer to Fatwa 87361. Likewise, if the parents of a child are Muslims, then he is a Muslim, and it is an obligation to wash him, perform a funeral prayer on him, and bury him in a Muslim graveyard. For more benefit, please refer to Fataawa 89073 and 85432.

Finally, we advise you to invite your Christian neighbour to Islam and clarify to him that the trinity is wrong, as Allaah may guide him thanks to you and you will get the reward of that on the day of Judgement.

Allaah Knows best.