General Conversations

I recently received a PIP letter where a major part of the narrative was simply a lie. Specifically, the letter spoke of how I had gone into another office, disregarded a supervisor's instructions, and told other employees to perform an improper task. This simply never happened. I had gone to this office to attend training and had nothing to do with what the employees there were doing. I later learned that two days before I had received the PIP one of my managers had gone to this office late in the afternoon, essentially "looking for dirt", asking all the employees there what I had been doing, saying, and then essentially then concocted this story used on the PIP. Is there anything I can do? The Union is not being very helpful. I have considered speaking to our Inspector General's office but I'm not sure if that would help or hurt the situation.