What actions are technically considered assault, and how can someone be charged with it.

A roommate of mine deliberately left the gates to our yard open in an attempt to let my dogs out of the yard. When I confronted him about why he did it, he ignored me (he's told me before that because I am a woman and he's a 'man' he doesn't have to answer to me). I followed him down the hall to his bedroom and tapped him on the shoulder and repeated myself several times, he continued into his room without answering me and I remained outside of his room while he grabbed his skate board. When he exited his room I was still standing in the hall and repeated my question, he scowled at me and pushed me out of his way, into the wall, to walk past me. I've since told my landlord what happened and he is being asked to vacate the house, it's not an eviction because he's agreeing to move out after the first notice. But he is threatening to have me charged with assault because I tapped him on the shoulder, which he first said were "jabs" and now is calling "punches". Another roommate (who has had problems of his own with this guy destroying his property) and a friend of mine were standing there and witnessed the whole thing are backing up my version of events. My only question is: Can he actually have me charged with assault or is that no longer an option because this happened a few days ago. I thought that assault charges had to be charged by the police at the time of the altercation. I know that his pushing me DOES classify as assault, but I decided to tell the landlord and have him removed from the residence as opposed to getting him charged with anything, because I know his intent was to get past me and not to injure me (if he had wanted to he could), but living with him any longer is not an option because he deliberately endangers my pets, and has no qualms about destroying others personal belongings.