Is it permissible for a Muslim to have a relationship with a Christian girl, given the fact that the nature of his work necessitates this relationship?

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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Friendship between a Muslim and a disbeliever is impermissible, according to texts of the Quran and the authentic Sunnah, which forbid affection for disbelievers, since this may lead to inclination towards them and satisfaction with their religion. However, this does not mean being unkind and unfair to them. 

Also, we draw your attention to the fact that if this relationship is between a man and a woman then it is even more impermissible, even if it is with a Muslim woman.

Allaah Knows best.