There are very few females on this planet that can dodge or withstand a swing from a man yet still manage to grab your hair in the process. They are complete weaklings. But that's using logic.
I've been in a similar situation with a female relative. She started belittling me to one of my friends and to made subtle, plausible deniable power ploys to undermine me in front of peope for no reason whatsoever. I wasn't even engaging her in conversation. I rarely speak to her. I often go the extra mile not to.
While alone, she got too close to me and I nudged her with only one finger to the shoulder, certainly not enough force to cause pain or lose her footing. She let out this exaggerated 'ow' and started to get pissed off. Instead of physical retaliation, she resorted to what women are designed to do, social violence. Later I overhear her telling people that I'm regularly abusive. I couldnt believe what I was hearing. It was complete bullshit, I rarely interact or speak with her....
She tried speaking to me after seeing my lack of reaction but didn't answer. I never justified myself to the people she told. I did not give her the emotion she craved. It would have been used against me anyway. I then confronted the other relative I was living with about the situation. Luckily, the truth came out and I was beleived and sympathized with. The people she told never spoke a word of it because I have a good reputation. The accusations didn't match my character I present to them.
Do not argue with her or try to use logic, it wont work. Remember, this is how women argue. Even though its a false accusation, your side will be perceived by onlookers as a loss of frame, and anything following this perceived event wont matter. The emotion you evoke, not your argument, will be used against you. She will teist your words and screw you over to save face. The way to deal with it is to not give her validation. She wants to get a response out of you. Women cannot instigate without an emotion to work with. Just let it blow over and stay away from her.
You're going against a 'victimized' uterus bearer in need, you are guilty until proven innocent. Others think she wouldnt make such a fuss if you didn't do something wrong. Do not try to call her out by suggesting she call the police. If she does, you will be arrested without any investigation due to primary aggressor laws. Police and the justice system are the ultimate whiteknights looking to fulfill their arrest and jailing quotas for privatized prisons.