What do I do about my neighbor assaulting me?

I threw a halloween party on Saturday night, it’s the first party we have had at this new house, and it was under control (the cops even turned up- were called- and I talked to them personally and they said everything was fine). Most people were well behaved, because they know my partner will kiII them if they pis me off haha.

Anyway. We were hanging out on Sunday after the party and some friends come over and come up to us and say there is an angry lady outside wanting to talk to us. I went out to her and my flatmate popped her head outside a window looking to the outside. This obese woman who lives 2 doors down just marches up and starts swearing profusely at me, calling me the most offensive words in the english language, and screaming at the top of her lungs. I stood there stunned as my flatmate speaks up and tries to find out what’s going on, asking the woman what she’s going on about. The woman starts on at my flatmate and start yelling about how we had a party and she didn’t have any warning. My flatmate was trying to explain that we didn’t think to do that but the party really was under control etc and the lady got really angry still swearing and yelling disgusting things at us. My flamate and some friends who had come over by now got pised off at her once they realized what was going on and started to raise their voices a bit. The woman was giving it lungfuls saying about how she’s ‘’going easy on us’’ and if she had it her way ‘’there would be an ambulance here by now’’ etc. I took a step toward her (she’s on our property) and said ‘’Is that a threat????…???’’ and she grabbed my upper arms, pulled them beside my body, shoved me into a wall and screamed into my face ‘’I KNOW WHERE YOU LIVE! I’LL FING COME BACK WHEN YOU LEAST EXPECT IT AND RIP YOUR FING TEETH OUT YOU LIL ST’’ and I was like what the f* and her husband came out and dragged her off me and back into her house. Meanwhile my flatmate had called the cops who came and got statements and came back to us with the excuse that she is tired and has a baby. They gave us a form to fill in to get a restraining order on her so that she can’t come on our property. But a lady I talked to today said that we could take the crazy woman to court for assault, that even if a person hints at intent to assault you it is considered ‘assault’’ so actually physically assaulting somebody is a blatant crime. I am in New Zealand so we have our court systems but who could give me any advice on the whole situations as to what me and my flatmates should do? We have 6 witnesses, 3 of which don’t live at our house.