As you know The Holy Quran is a word of God and it demands respect. If you think that the person whom you are going to give a Holy Quran will respect it and he/she is really serious to learn what exactly Quran is? What is in Quran? Want to understand Islam as a religion then it is allowed because this is a great way to spread Islam’s message to non believers, He/She can also compare Holy Quran with there own religion books,

If non-Muslim don’t understand the Arabic then it would be better if you only give holy Quran’s translation to him/her and not the Arabic Quran with translation. If in some case you are going to give him/her Arabic Quran with translation then recommend them to purify before touching it. Tell them the way to purify themselves, how to handle Quran in best way and teach them as best as you can so after that if there any neglection happen then there is no blame on you.

But it is extremely not allowed to give Quran to non-Muslims, if you think that he/she is a narrow-minded person and there might be a chance of disrespect to Holy Quran and Islam as well. You just need to check these things first before doing anything.