What can happen if someone files a complaint against you that is listed as "a criminal threat"?

If you are found guilty, you could have a rathr hefty fine. If you get a nasty judge, you might even serve some jail time. If depends upon the severity of the threat, the ability of the person making the threat to actually carry it out, and other factors.

Pretty serious stuff

A “criminal threat” is when you threaten to kill or physically harm someone and that person is thereby placed in a state of reasonably sustained fear for his/her safety or for the safety of his/her immediate family,

the threat is specific and unequivocal and
you communicate the threat verbally, in writing, or via an electronically transmitted device. Criminal threats can be charged whether or not you have the ability to carry out the threat…and even if you don’t actually intend to execute the threat.
Examples
1) threatening to shoot another person while you are holding a gun,
2) a recently fired employee calling the former boss and saying “you and the office staff better watch your backs,
3) texting your ex that you’re going to set fire to her apartment.

I know someone who did 3 months in jail and got $2,500 fine and was put on 3 year’s probation because he e-mailed his ex-wife a news story about a guy that killed his ex-wife.

How about if you say you are going to kill someone who you know has access to a gun because you are hoping they will shoot you and kill you? I guess if they were a very strong tough guy person and you were a puny wimp they would know they could easily kill you so they wouldn’t care what you said, whether or not they responded by shooting and killing you would depend on what kind of person they were. You may hope they would shoot and kill you because you knew they could maybe they are a Hero to you for some reason and having them shoot you in the head and kill you is your way of saying you respect them.