She at the very least wants it to appear to be fake. The first part of chapter 10 in her book, "Full Disclosure":

I was then given yet another statement to sign. I sat up to read it. “The fact of the matter is that each party to this alleged affair denied its existence in 2006, 2011, 2016, 2017, and now again in 2018,” the signed statement read. “I am not denying this affair because I was paid ‘hush money’ as has been reported in overseas-owned tabloids. I am denying this affair because it never happened.”

I panicked. I admit it, I panicked. I didn’t know who the Gucci guy was. Was he the one threatening me? Did he have a gun? Even though I knew the statement was complete bullshit, I picked up the pen and signed my name. But I purposely signed it wrong. “Stormy Daniels” has a very distinct signature. I have signed my boobs on magazine covers for many years. I signed the statement like it was my first day as a grown-up, girly and bubby. I wanted to signal there was something amiss here.

My girlfriends showed up. I didn’t say a word to them, and if I seemed shaken to them, they probably thought I was uncharacteristically nervous about going on live TV. In no time, Michael Cohen had the statement, and he released it three hours before the show. Thanks, Keith Davidson. Always advocating for his clients, that guy.

Jimmy had a printout of the statement at his desk, and with no tip-off whatsoever from me, he brought up the signature right away on the air.

“This is what fascinates me,” he said. “The signature on your original statement does not match the signature on this statement.” He pulled out a bunch of signed photos he’d found on the internet as examples of my real signature. “Am I getting at anything? Did you sign this letter that was released today?”

“I don’t know, did I?” I said. “That does not look like my signature, does it?”