Boss Told Me He Falsely Turned Down A Promotion I Was Offered (ny)

Boss let it slip in a moment of anger that when I applied to go from a floor warehouse associate to administration I was offered the position but he told them I refused it. It's not a monetary raise but its the difference between being just a worker and management.

I went over my hrs head to the regional hr as my local hr likes to sweep things under the rug with my manager. And it will be investigated, but what else do I need to do? Was I right to contact my employer, should I be looking for a lawyer? This is all just bits to a much grander level of bullying and harassment.