As with your driving record they will run a criminal history through the National Crime Information Center to see if you have a criminal record. Nearly every police agency will not hire you if you have been convicted of a felony charge. A misdemeanor conviction does not necessarily disqualify you for the job. They will inquire as to what type of sentence you received. They will ask you about the details of the case. If this was something you did as a juvenile, then share that with the panel. Their concerns are whether or not this is the only time you were caught. If you were arrested but the charges were later dropped or you were found not guilty, they will question you concerning the charges.