You don't say which hotel this was, but I would write directly to their home office. If it is a reputable chain, like Hilton, Ramada or Marriott, I'm sure they will do the right thing by you.
If push came to shove, the hotel could insist that you pay just the correct rate. They could say that a mistake in billing, even if intentional, should not entitle you to a free stay in the hotel. That kind of position of course would be bad customer service, but not illegal.
No, of course forgery is illegal. But there are two issues here: the first issue is that your signature was forged and that you were billed a higher rate. The second issue is, do you owe Marriott for a stay at the correct rate?
Since you documented the incident with the police, I think that if you were to bring this entire incident to the attention of Marriott's home office, they would do the right thing by you.
It depends on what you want Marriott to do about it. Forgery is a crime. The appropriate action would be for the police to investigate, and arrest the desk clerk if they determine that there is probable cause to believe he committed a crime. If they choose not to arrest the desk clerk because they find no probable cause to make an arrest, then the forgery is simply a civil matter.
You could sue Marriott over the forgery, but you would have to show that you were damaged somehow. If no money was taken from you because of the forgery, then you have no damages. If, however, you were charged a higher amount because of the forgery, then you do have damages, and maybe even a claim for punitive damages, but only if you could show somehow that Marriott should have known that this employee had a criminal history or had done this before.
I would see, first, what Marriott Corp. is willing to do for you.
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