You might be talking about first offender status. Many municipalities in Wyoming allow people to apply for first offender status if this is the first crime they've been charged with and they have a good reason for needing it. After the successful completion of first offender probation you can have the record expunged. It is often a few years on probation. You can apply with a standard form provided by the court and approval of the prosecutor.
If you have been charged with a misdemeanor and it is more than (I think) seven years since you have been in trouble, you can apply to have your record expunged. The forms for this are usually available at the courthouse and were online at the state department website last time I needed them.
You should talk to a lawyer about this. If you can't afford a lawyer go to the public defender's office and talk to a lawyer there. A lawyer should be able to help you get things sorted out.
Best of luck,
Shannon K. McDonald