What are my rights if my pay was cut as punishment for an unsubstantiated complaint?

Question Details: I used to be in a supervisory position at my job. About a month ago, I saw an employee in violation of a department policy and I advised them to comply with the policy and they complied although in protest. Then, 5 days later, they attempted to break the same policy and I confronted them again, this resulted in another supervisor and my supervisor getting involved. The next week the employee made a complaint to me with our HR department. I met with HR and I was not fully informed of what the complaint was but based on the questions I assumed she complained that I stalked her at work over the compliance issue. I denied having followed her at all during the incident. About 2 weeks later, I was called to a meeting where I was still not informed of the reason for the complaint but I was told I was being reassigned to a non-supervisory position and my pay would be cut but it would be due to department reorganization resulting from the incident and my old position was being eliminated completely. As best I can tell she received no punishment. Later I found out that there was video evidence proving I had only been in contact with her for 4 minutes over the 2 hour period this event occurred but HR had not made any attempt to review this footage or determine if her accusations of me stalking her were true. I'm now looking for another job and would like to know if I can take any legal action against my employer or co-worker.

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