I think it all depends on the state or city you live in. You could go to school for it, and then when you do a background check for a job in that field and it shows up, you can explain the misdemeanor to them. I don't think a misdemeanor is bad, because my brother had that same misdemeanor many years ago and he still became a police officer. so yes, I'm sure you can because it's only a misdemeanor. Felony is a different story. :)
When considering a career in criminal justice, you have to bear in mind that what you’re dealing with are the most highly sensitive information of all cases. Background checks are standard. These are the "must look" to trace for any discrepancies in your life, especially for a criminal record. A misdemeanor may disqualify you from becoming a crime scene investigator. But, who knows. It could also depend on the qualifications set by the criminal justice agencies who may want to consider minor offenses.