@Gina29....How do you know this 'guest' is using a stolen credit card?
The police will not want to get involved unless their is a safety issue involved, and I doubt highly that Airbnb will want to be involved either! They will simply dither around and pass the buck around the office until the problem disappears. Report it to Airbnb but I would not expect a satisfactory resolution, but at least the report will be on file.
If you are sure that the card is stolen and have access to the card details I would contact the card company, explain your situation and ask their advice. Even if you don't know the card details but have the card holders name still contact the card provider. In most instances card providers will wear losses where innocent parties are involved!
Cheers....Rob