Can police send me a letter saying I owe money when I have never been to court?

Yes, if your failed to appear in court you will be subject to a default judgment and a warrant and/or fine can be issued.

This could be a scam. I would call the court where the warrant allegedly is and find out if it is true. I will say that a surprising number of people are completely unaware of warrants in there name so it could be real.

I would agree that you should call the court to confirm the warrant and the nature of the underlying charges. Just because you have never been in court does not mean you weren't supposed to be. Perhaps you never received notice to appear? Maybe you forgot about a traffic ticket? While the notice you received could be the product of a mistake or a scam, "failure to appear" provides legitimate grounds for a court to issue a bench warrant. It would be wise to clear this up as soon as possible. If you confirm that there is an active warrant for your arrest, you should consult with a criminal defense attorney in Montana as soon as possible.