If I am arrested for drug possession, is there a way to have my criminal case dismissed?

Yes. Certain drug offenses, excluding trafficking, may allow you to qualify for the Specialty Courts Diversion program. Division court places you under the supervision of the State and Court but allows you, after successful completion of the supervision, to move to have the charges dismissed and the record of the offense sealed. There are different programs available under Nevada law and you should discuss whether you are eligible and which program might be best for you with your attorney.