If the check hasn't yet cleared their bank, they can put a stop payment on it. That means that if you either haven't cashed the check yet or you have cashed it but it hasn't arrived at their bank yet, they can revoke the check. The fact that they signed it is of no consequence. A person can tell their own bank not to cash a check that draws on their account. If the check has already cleared their bank, then to recover their losses, they would have to either get you to agree to reimburse you or sue you, like in small claims court.
As for the police, if you defrauded the person, they can certainly get the police involved. If you didn't defraud them, if you committed no criminal act of misrepresentation in order to extract money from them or any other criminal act in association with the sale, then any attempt to get the police involved will certainly fail.