Does a PhD student need a co-supervisor? I am a few months into my PhD and my supervisor and co-supervisor are close friends. 

Unfortunately, I find that my co-supervisor is not useful – he doesn’t provide any help or input into my project. Additionally, he has given me a hard time on more than one occasion, e.g. making a derogatory comment about the source of my PhD funding, not including me in discussions with his other PhD candidates (although I was physically present), and asking me to buy items for another PhD candidate using my budget.  

I would like to stop being supervised by my co-supervisor, but I have not yet built a relationship with another academic that I could ask to take the role. 

Do I need a co-supervisor? Can anyone recommend ways I deal with this situation?
The direct answer is not a PhD students does not need a co-advisor. The problem here is to think about the role of co-advisors. I am sure the view on this varies so my view is coloured by situations with which I am familiar, which is the US and Sweden. Co-advisors may be involved because they have specific expertise that may be relevant to part of the work, for example specific investigations, lab work ec. Co-advisors may also be there to provide overall scientific expertise and provide feedback on written articles or the final thesis or both. Hence a co-advisor may not be very active when you start your PhD. At the same time by signing up as a co-advisor, I would expect the co-advisor to be open for discussion during your time as a student but it may fall on you to initiate such contacts when you need it. The main advisor is, after all, the one responsible for the direction of your work within your thesis topic.

So while one does not need a co-advisor, there are many instances where such support is necessary or at least very useful.