If you don't want to do something, you normally use "refuse".
example: I refused to talk to him. (perhaps it was offered, but I didn't want to do it and I didn't).
If your answer to something is "no", then you use "deny".
example: They said I'd robbed the bank but I denied it.
If you don't want to address a question or person, you ignore it.
example: He was being annoying so I just ignored him.
I hope it helps