I agree with ringlet, it doesn't so much sound like symptoms of depression and anxiety, but a bit of an awkward character. You've been put in a bit of a difficult position, if you are all managing each other, really.
If you don't already, it might be worth having regular meetings between you all, so everyone gets a chance to say anything bothering them, without singling him out. It might be some simple underlying reason, such as he (rightly or wrongly) feels he gets the "worst" jobs or something...
Also, make a record of anything he refuses to do or causes problems with, so if you have to bring it up with him, you have some proper facts you can show him.
If it really is just attitude, you can only really befriend him and see if you can work out if there is anything particular that does need changing. Communication really.