My question involves criminal law for the state of: California
The other day after doing some shopping at a Wal-Mart, I was stopped by Loss Prevention(I don't believe they officially introduced who they were), on my way out with my cart of purchases, and the LP lady said that the shirt I had on was not my shirt; that they have my "real" shirt, and for me to come with them. They asked me for my I.D which I gave to them and they took me to a backroom, where I guess they monitor the cameras in. They had me empty my pockets, and asked me if any of the stuff in my pockets was stolen, I told them and said no. They took down my I.D. Info and asked me for my social security number, which I gave them, thinking this is ridiculous, they'll realize their mistake soon enough. They told me if I'm truthful, they'll have me out of there quick. They said that they're gonna bring in what they called my "real" shirt. I took a look at the shirt I had on thinking, "Oh man!, did I accidentally switch one of the button shirts I took into the dressing room with the dress shirt I came into the store with?". But nope! The shirt I had on had the food stain that it always has(I'm on the poor side and haven't really had a "life" for awhile, so my clothes are never too clean), it was indeed my shirt, the one I wore to the store that day. I mentioned the stain but they said it's because I had been wearing it awhile. And then thinking back, I realized I didn't even take a shirt quite like it into the dressing room.
I kept denying it, but they just kept repeating that "We don't make mistakes. Not me." and "I've been doing this for a long time, I know what I'm saying". They said they had been watching me for a long time. And said "I'm sure you've known", which I didn't. Anyways, long story short, I eventually ended up leaving, they took my photo. And they said that I'll receive a letter to pay for the shirt I "stole", but is actually the one I came in with(I'm guessing they mean a civil notice). I asked them if I could see the video footage, but they said they're not allowed to. I asked them that couldn't they just look at the video themselves and see the shirt I came in with. They said I had my sweater zipped up when I entered. I told them that I never zip it up all the way, and showed them that the collar always sticks out, that couldn't they take a close look or something, but they didn't say anything.
I am wondering, what I can do. They said they'd send a civil notice. Do I call the police to investigate and find the truth? Do I contact a manager or something with my story, maybe he/she'll listen? Because I stole absolutely nothing, and do not want to stand for receiving a bill for my own shirt. Thanks for any advice.

