Being kind and professional is the most powerful

weapon to protect yourself in this situation, especially you are new to the company.  Bottom line, don't say any negative and bad things about anybody. 

If the person is really bothering you and has negative influence on your work performance, when someone like your manager asks you, you can say that you are concerned that there might be some misunderstanding or miscommunication....bring it up in a way that people wouldn't think that you treat it personally but look for solutions.

I wouldn't report it without being asked as you will have a record from your reporting as well that you and that person doesn't get along unless you have strong evidences on paper, unless that you are sure you wouldn't have any conflicts with anyone else in the future in the team.  

Just my two cents from my experience and good luck!