Blocking and receiving gifts

My BD had never been in baby's life (his choice) He isn't on the BC but every now and again I get grief from him over text, threats with court , he has a violent history which I didn't find out about until further down the line, he is a classic narc. Anyway can I get into trouble for blocking him permanently? He has no contact with baby like I say (he has just turned 1) what he also does is send random gifts to my house do I accept them or refuse them? As he has my address obviously. What would you do about gifts? He sent him xmas and birthday gifts. Further down the line this is going to he confusing for him reveiving gifts from his dad who isn't in his life? Any advice? There's always a chance he will take us to court too but still waiting...