I've been accused of verbally abusing a resident. How do I handle this situation?

With honesty.
Perhaps you are innocent but I know that there were many moments when I was in the trenches as a full time caregiver that I was glad nobody had a nanny cam to record my low points - meltdowns happen, especially when we are asked to do more than we physically or mentally can. You are naturally going to feel defensive when confronted about the accusation, it might help to have a written timeline of things from your perspective as well as a proactive summary of what you feel can be done to ensure this won't happen again. In a work situation this could be an opportunity to ask for and get more training in whatever caused the conflict - responding to dementia behaviours, conflict resolution, proper use of assistive devices or perhaps anger management....

I don't know the specifics of your situation, but I can tell you from seeing my mom and her cohorts in their dementia care assisted living facility that ANYTHING you say can be misconstrued by a dementia patient. They have their good and bad days, just like everyone else, except that on their bad days, everything is magnified. If you don't smile big enough when you pass them in the hall, they go to pieces. When mom was living with me, she would tell people that I "yelled at her" all the time. She is hard of hearing and her hearing aids were useless. The only time I raised my voice to her was so that she could hear me; I never did it in anger. She lip reads for the most part and often assumed I said something I didn't. She tended to embellish on her accounts of events and conversations before she had dementia, it just got worse afterward. I frequently found friends and family angry with me and had no idea why until they told me of things I supposedly said to mom. My brother and sister and I had always had a good relationship until mom started arguments between us by misquoting us to each other. Now that she is in the facility, she often starts trouble between the staff members there and between our family and the staff. I used to stress over it, but now try to just ignore it. I always look into her claims of mistreatment, but I've learned to take her accounts of verbal abuse with a grain of salt.

What did you say?
How did you say it?
How often did you say it?
What was your tone?

We're going to need more information if we're to help you handle this situation.