Criminal Law Questions? Ask a Criminal Lawyer.
Filing a false report is a crime. Sometimes this is prosecuted and sometimes it isn't. It usually depends on the severity of the report and how much the report resulted in wasted resources (police time, court time, accused expenses, etc...)
If you have been falsely accused of a crime, you can also file a civil suit for defamation of character and/or malicious prosecution. This civil action can be quite damaging against the person who made the false report (financially damaging).
You should speak with an attorney in your district if someone has made these allegations against you.
I am not your attorney. This forum is for general questions and answers and I cannot provide you with applicable law or legal opinions or advice in your jurisdiction. Please seek the advice of a competent attorney in your jurisdiction. While I can answer general questions and discuss general legal principles, I cannot give you legal advice in your state. The internet is a great place to get general information but should not be seen as a substitute for the attorney-client relationship or the services of a good lawyer in your state.
That depends on the specifics of what was reported to the police. There are several crimes where someone makes threats... the specific crime would depend on the type of threat, the circumstances surrounding the threat, and the method of communicating the threat.
All of these things can (and should) be investigated by a local attorney without you having to incriminate yourself by speaking to someone with the police. You should allow a local attorney to look into this as it will likely be very inexpensive and you would be protecting yourself in the best manner possible.